Uber and Lyft are locked in a high-stakes battle for market share. But new data suggests that Lyft still has an uphill climb in its quest to compete on a level playing field with its larger, richer rival.

About three-fourths of Lyft users also hail rides with Uber, but only a little more than a quarter of Uber users also take trips with Lyft, according to four months of app data analyzed by Survey Monkey. Also Uber is outpacing Lyft in the average number of daily downloads of its app, 100,000 versus 25,000. Survey Monkey pulled the data to showcase its new Intelligence product that tracks app usage across tens of thousands of users who have agreed to have their mobile behavior tracked.

The data is especially noteworthy in light of Lyft CEO Logan Green's recent comments to the Wall Street Journal. When asked what sets his company apart from Uber, Green responded, "We treat people better. When the driver enjoys driving and working with Lyft, that shows. They're happier. Every pickup they do, they're in a better mood. And they feel encouraged to go above and beyond and treat passengers better. When you get the same basic service level from both companies, more people are choosing to support the company whose values they align with."

"When you get the same basic service level from both companies, more people are choosing to support the company whose values they align with."

Indeed, Lyft has been gaining momentum lately. It recently struck a high-profile partnership with General Motors to develop a fleet of autonomous, on-demand vehicles. Its ridership in New York City has grown 500 percent since May 2015, the company told Re/code. And it plans on expanding its carpool service Lyft Line in a half-dozen US cities, outpacing Uber in the process.

But Lyft is still unable to pull even with Uber. Lyft's valuation, $5.5 billion, is a fraction of Uber's $62.5 billion value. Meanwhile Uber lured its smaller rival into a costly price war this winter. It slashed its fares in over 100 US cities, forcing Lyft to respond by similarly reducing its prices in over 30 cities. This set off a wave of discontent among drivers, many of whom are struggling to earn a living while juggling shifts for both ride-hail companies. (As independent contractors, drivers are not required, nor are they encouraged, to drive for just one service.) Uber recently started to raise its fares in some small- and mid-sized cities, and it remains to be seen whether Lyft will too.

Lyft users lack loyalty

That said, Green made an excellent point in his interview with the Journal: Uber is burning through mounds of cash by trying to compete in new markets in India and China. "I think they've picked a number of losing battles, and they're paying a pretty high price for that now," Green said. How high a price? Uber CEO Travis Kalanick recently said his company was losing $1 billion a year in China alone.

Lyft only operates in the US, but recently struck a deal with Didi Kuaidi and Ola, the dominant ride-hail companies in China and India, respectively, so its users can hail rides when traveling abroad. But given the lack of loyalty among Lyft users tracked by Survey Monkey, all the global partnerships and self-driving cars in the world may not be enough to keep them away from Uber.