Do you get the best prices trading stocks?

It was among the millions of trades made by individual investors that day. The Houston resident’s order didn’t go to the New York Stock Exchange or Nasdaq Inc., where buyers and sellers haggle over the company’s shares.

Instead, TD Ameritrade sent Mr. Hanson’s order to Citadel Securities, an electronic trading firm that deals directly with brokerages to execute their customers’ trades.

Within milliseconds, Citadel Securities bought Mr. Hanson’s Immunovant stock for $5.0221 a share—an improvement over the best price quoted on exchanges, where buyers were offering $5.02 for the shares.

The result: Mr. Hanson made an extra 21 cents, earning $502.21. Meanwhile, Citadel Securities paid TD Ameritrade a slice of its profit from handling the order, a practice called payment for order flow. Regulatory filings suggest the broker got about 10 cents.

Did Mr. Hanson get a good deal? Proponents of payment for order flow cite gains like his 21 cents as evidence the market works well for small investors. Critics say the practice has so warped the market that it’s impossible to say what Mr. Hanson, who works in financial services, would have earned in a truly open marketplace.

For years, that debate was largely academic. But it’s now at the core of a showdown between powerful trading firms—Citadel Securities chief among them—and a Securities and Exchange Commission chair who views them warily.

On Wednesday, the SEC is set to propose the biggest shake-up of U.S. stock market structure in more than a decade. Chair Gary Gensler has said he wants to give investors a better deal on stock trades by forcing greater competition for their orders. The proposals grew out of a review prompted by the frenzied trading in GameStop Corp. in early 2021.

They will likely stir up a hornets’ nest of opposition. Brokerages and trading firms say there’s little evidence the current system hurts investors. Some firms, including Robinhood Markets Inc., have signaled that they could sue the SEC if Mr. Gensler’s changes go too far.

Last year, the 12 largest U.S. brokerages collected $3.8 billion in payment for order flow, according to Bloomberg Intelligence. The largest source of the payments was Citadel Securities, which paid out just under $1.5 billion.

At Charles Schwab Corp., the parent of TD Ameritrade, Jeff Starr, a managing director, said, “When you see the sort of execution quality that we’re getting, it’s really hard to say that payment for order flow is a problem.”

Citadel Securities, though lesser-known than its sister company Citadel, a $59 billion hedge fund, is a behemoth that handles more than 20% of the shares that change hands in the U.S. stock market each day.

Both firms were founded by billionaire Ken Griffin, known for his art collection and trophy homes, including a $106.9 million waterfront estate he recently bought in Miami. He is also a Republican power broker. Since 2021 Mr. Griffin has given more than $68 million to federal campaigns, making him the country’s third-biggest political donor, according to OpenSecrets.org, a nonprofit that tracks campaign spending. On Tuesday, he sued the Internal Revenue Service and Treasury Department seeking damages over a tax privacy breach.

The controversy over GameStop’s January 2021 extraordinary rally and crash thrust Citadel Securities into the spotlight. At the time, Citadel was the biggest processor of orders from Robinhood, prompting a widespread conspiracy theory that Citadel Securities used its influence to halt the meme-stock rally. The firm denies doing this. Still, Mr. Griffin was challenged about his firm’s role in the episode during a contentious hearing of the House Financial Services Committee, where he was grilled by the committee’s chairwoman, Maxine Waters of California, and other Democrats.

Since then, his firm has been less outspoken in criticizing the SEC’s plans than other industry players such as rival trading firm Virtu Financial Inc.

“Citadel is a little bit handicapped because Ken is kind of a lightning rod right now politically,” said Virtu Chief Executive Douglas Cifu. Citadel Securities instead has pressed its case against the SEC’s overhaul at industry conferences and in closed-doors meetings with regulators.

Mr. Griffin met with Mr. Gensler in June 2021 and discussed a Citadel Securities white paper on market structure, in which the firm outlined a set of changes less radical than what the SEC is now planning, people familiar with the matter said. In March, a team from Citadel Securities met with staff from the agency’s trading and markets division, according to people familiar with the meeting. A presentation from that meeting, seen by The Wall Street Journal, touted the firm’s ability to deliver savings to investors.

In an interview, Mr. Gensler said investors would get better prices on their trades if there were more competition between trading firms for their orders. He acknowledged that his plans could hurt the profits of brokers and trading firms.

“Putting folks in competition is better for investors and issuers,” he said. “It might have a tendency to lower some of the economic rents in the middle.”

Citadel Securities will await details of Mr. Gensler’s proposals before deciding how hard to fight them, said Joseph Mecane, the executive who leads the unit of the firm that processes trades for retail brokerages.

“We’re quite proud of the experience that’s been developed for retail investors,” Mr. Mecane said. “Anything that, in our opinion, would impact the retail experience in a negative way would be something that we worry about.”

Executing trades for individual investors is lucrative for firms such as Citadel Securities because it is more consistently profitable to fill individuals’ orders than to trade with the large, sophisticated investors the firms encounter on public stock exchanges.

Citadel Securities, Virtu and similar trading firms earn money by market-making—the strategy of capturing the difference between the buying and selling price of stocks, known as the bid and the ask.

Market-making is risky on exchanges because institutional investors are big enough to push prices up or down. If a hedge fund is selling millions of dollars of Ford Motor Co. stock, it could chop up the transaction into hundreds of sell orders over several days. A market-maker offering to buy Ford could lose money as it buys over and over, while the big seller drives the price lower.

That makes it attractive for market-makers to deal directly with brokerages such as Robinhood and TD Ameritrade. The customers of such brokers place orders that are typically smaller and more balanced between buys and sells.

Individual investors benefit. Market-makers can offer better prices when they know they’re only facing the little guy, giving sellers like Mr. Hanson higher prices for their shares, while giving greater discounts to buyers of shares.

Traders call this phenomenon “price improvement,” and industry data show that individual investors collectively save billions of dollars a year as a result. In addition, thanks to payment for order flow, nearly all major brokerages have shifted to zero-commission trading since 2019, versus the fees of roughly $40 or more they charged a few decades ago.

Critics of payment for order flow—a mix of Wall Street veterans and advocacy groups pushing for tighter regulation—say the practice creates a conflict of interest. If brokers get paid to route orders, critics ask, are they really putting their customers first?

“At the heart of it, you’re putting a perverse incentive out for the firm that is supposed to be working the hardest to get you the best possible price that they can,” said Doug Atkin, former CEO of brokerage Instinet. “Payment for order flow, at a minimum, clouds that.”

They also say the benefits of the current system are overblown. The reported savings that brokers deliver their customers is based on the difference between the price an investor gets for a stock and its publicly quoted bid and ask price on exchanges. Some analysts say that benchmark is flawed because about 40% of trading volume, including many individual investors’ trades, takes place outside of exchanges.

BestEx Research, a trading-technology firm, estimated in a report last year that if all retail orders were sent to exchanges, bid-ask spreads on exchanges would narrow by 25%. Since the current system makes those spreads artificially wide, the savings that investors receive are inflated, the firm said.

“Price improvement on retail market orders is akin to getting a 30% discount on an item after the shopkeeper raises the price by 40%,” BestEx Research wrote.

Could Mr. Hanson have gotten a better deal? Some analysts who reviewed the data on his trade say it’s possible. For instance, some exchanges allow buyers and sellers to do “midpoint” trades at the price in the middle of the spread, in this case between the $5.02 bid and $5.04 ask. By selling his Immunovant stock at the midpoint, Mr. Hanson would have earned $5.03 a share, or $503 in all. That would have yielded him a gain of $1 instead of 21 cents.

Executives at brokerages and market-makers have questioned the methodology of the BestEx Research paper. Schwab said it got midpoint executions or better on 52% of its customers’ market orders last year.

Payment for order flow emerged in its current form in the 1980s, when it was championed by Bernie Madoff. Decades before his conviction for masterminding a vast Ponzi scheme, Mr. Madoff led a firm that paid retail brokerages for orders and executed them off-exchange.

In 1994, the SEC adopted a rule that required brokers to disclose whether they were receiving such payments. The agency revisited the practice in the decades that followed but always stopped short of a ban, choosing to step up disclosure requirements instead.

Mr. Griffin founded Citadel Securities in 2002 at a time when the transition from old-fashioned trading floors to electronic marketplaces was creating new opportunities for computerized trading. The firm was initially called Citadel Derivatives Group and focused on options market-making.

It urged the SEC to ban payment for order flow in 2004. “This practice distorts order routing decisions, is anti-competitive, and creates an obvious and substantial conflict of interest between broker-dealers and their customers,” Citadel wrote the agency in a letter. Mr. Griffin has said the letter reflected Citadel’s concerns about the options market at the time.

Citadel soon began paying for order flow to break into equities market-making. Former employees say Mr. Griffin was determined for Citadel to win business from big-name brokerages such as Schwab. Citadel positioned itself as a high-tech disruptor, honing its algorithms to give better trade executions than rivals, the former employees said. It had a breakthrough in 2005 when TD Ameritrade agreed to start sending it orders.

By the Covid-19 pandemic, Citadel Securities was handling as much as 47% of U.S. individual investors’ stock-trading volume. It had grown into a global market-maker in futures, Treasurys and currencies with revenue of $7 billion last year, a person familiar with the matter said.

In January 2021, investors banding together on Reddit ignited a tremendous run-up in shares of GameStop and other meme stocks—only to see the rally collapse when Robinhood and other brokers temporarily blocked customers’ ability to buy the stocks. Many social-media users embraced the theory that Citadel Securities had spearheaded the decision to remove the buy button.

Both Citadel Securities and Robinhood denied this. Robinhood said it made the unpopular decision after the clearinghouse for U.S. stock trades demanded billions of dollars of collateral amid the mounting volatility. A congressional report in June confirmed that explanation.

Nonetheless, Mr. Griffin was vilified by an online movement of investors calling themselves apes, who trolled him with hashtags such as #CitadelScandal, and some paid for truck-mounted digital billboards to drive around big cities with slogans bashing the firm. “It was a bit of a surreal experience,” recalled Mr. Mecane.

Near the peak of the GameStop frenzy, the Biden administration chose Mr. Gensler as its pick to lead the SEC. Now he is pursuing the most aggressive agenda for an SEC leader in decades, including his proposed overhaul of stock-market structure.

Mr. Gensler has criticized payment for order flow, calling it potentially detrimental to the interests of investors, and last year he indicated he was open to the idea of banning it. He has also said the business of processing individual investors’ orders is concentrated in too few firms.

Citadel Securities says it wins a lot of retail order flow because it offers the best prices. Backing up that claim, a recent academic study based on 85,000 trades at several popular brokerages found that Citadel Securities saved investors more money through price improvement than any other market-maker.

Mr. Griffin has said his firm would be fine even if payment for order flow were banned. “Payment for order flow is a cost to me,” he said in a public appearance last year. “So if you’re going to tell me that by regulatory fiat one of my major items of expense disappears, I’m OK with that.”

Eliminating payment for order flow would be trickier to brokerages, some of which lean heavily on the practice as a source of revenue. Robinhood—which makes the bulk of its revenue from selling order flow for stocks, options and cryptocurrencies—indicated when it went public last year that new restrictions on payment for order flow could hurt its business.

In a June speech, Mr. Gensler appeared to back away from the idea of banning payment for order flow. Instead, he is set to unveil a proposal to funnel investors’ orders into auctions, in which market-makers would compete to give the best price on each trade.

Mr. Gensler’s agenda has brought criticism even from Democrats who might seem like his allies. “There would be no zero-commission trading without payment for order flow,” said Rep. Ritchie Torres (D., N.Y.), a member of the Congressional Progressive Caucus. “So my message to the SEC is simple: Don’t throw out the baby with the bath water.”

Supporters of Mr. Gensler dismiss such concerns as the result of industry scaremongering. “It’s your standard terrify-the-regulators approach,” said Dave Lauer, founder of market-data startup Urvin Finance. “They’ll say, ’You tinker with anything, it’s all going to come falling apart.’”

Many SEC watchers expect the industry to challenge Mr. Gensler’s proposals in court.

“There has been a secular trend in the last two decades toward an improved retail trading experience,” said Jason Clague, a managing director at Schwab. “What we’re struggling to understand from Chair Gensler and his staff is why they feel the market is broken, despite a wealth of evidence to the contrary.”

—Paul Kiernan contributed to this article.