The bitter battle between Uber and Lyft isn't exactly a close fight.

According to new research that draws on credit and debit card transactions by 3.8 million Americans, Uber's revenue was about 12 times that of its rival between May 2013 and May 2014. Across the U.S., it provided more than seven times the number of car rides, the report indicates, and it charged much higher rates for its service: $21 per ride on average, compared to Lyft's $13.

Headquartered not far from each other in San Francisco, the two startups provide practically identical services that seek to change the way people get from place to place. Each lets you hail a car—and pay for the ride—via a smartphone app. That means the two are fighting for drivers as well as riders, and as they tussle in major American cities, they've clashed in sometimes spectacular ways, with Lyft accusing Uber of using underhanded tactics to snatch its drivers and news stories indicating that these were far more than just accusations.

But judging from investments in these two companies—Uber is valued at about $17 billion, Lyft at $700 million—it seemed that Uber was running the more successful business, and this new study provides a window into just how big the gap has become.

The study arrives from FutureAdvisor, a San Francisco outfit that offers software for automating the management of your stock portfolio. But in this case, the company is exploring two companies on the verge of going public, using data from an unnamed outfit that pools information from major American banks.

James McQuivey, an analyst with the Massachusetts-based research firm Forrester, is hardly surprised that the study shows Uber out in front of Lyft. After all, he points out, Uber's ride-hailing operation had a significant head start (Uber was founded in 2009, while Lyft, in its current incarnation, launched in 2012). But he says the size of the revenue gap, as indicated by the new study, could help show why Lyft is so intent on waging a war with Uber in the media. "Lyft is trying to associate itself with Uber," he says, "trying to punch above its weight."

The FutureAdvisor study also indicates that Uber is acquiring new riders at a much faster clip than its rival, adding between 6,200 and 7,300 per month during 2014, compared to between 1,100 and 1,500 added by Lyft. But according to Casson Stallings, the data scientist that ran the study, both companies are growing at a significant rate relative to their size: roughly 10 percent a month. "Outside Silicon Valley," he says, "companies would be jumping up and down over that."

That said, as they've spread across various U.S. markets, Stallings says, the relative growth of both companies has slowed. In June of last year, each was growing at a rate of 25 percent per month. That could indicate why the companies are now fighting so fiercely over each other's drivers—and why Uber is so intent on expanding overseas.

Some reports have indicated that Lyft is looking to be acquired by Uber. But just this week, Uber CEO Travis Kalanick said his company has no interest in such a move. "We're not in acquisition mode," he said.

Update 12:32pm EST 09/11/2014: In a statement sent to WIRED, Lyft says the data set used by FutureAdvisor does not track the company's actual growth. The company says that this past May, its growth was 40 percent month on month, not 10 percent.