As someone who drove for both platforms, this is not true. Lyft pays drivers more than Uber in the market I was driving in.
Most drivers would abandon Uber in a heartbeat if Lyft just had more users. The problem was that for every Lyft request that came in, you'd get 10 to 20 Uber requests.
Lyft has an actual balance sheet Investors can understand.
Fun fact, I was an early and enthusiastic user of Zimride (for making a long distance relationship work between the Bay Area and SoCal). I liked the product and once upon a time drafted an e-mail applying for a position there. I assume I would have been employee like ... 5 or something. Never sent it and it hung out in my Gmail for many years. Decisions, decisions :-)
To me, the key change deserving a new term was allowing completely independent, non-professional drivers, and I think Lyft beat Uber to that. (Heck, some purists would say "ride sharing" should be reserved for cases where the driver doesn't make an wages, just reimbursement for costs.)
Uber launched UberX in June 2012. Lyft launched in June 2012.
Give Sidecar credit where it's due.
Then Waymo dozes over both of them while destroying a large chunk of the "gig economy".
The network effect favours the larger player: less dead-heading between rides and better “pool” load-factors.
Uber doesn't have a massive moat. Drivers can have both apps, users can have both apps. You attract drivers by paying them more, you attract riders by charging them less. Uber for now can afford to beat everyone on both those fronts, but eventually they will have to start making a profit. When that happens Lyft is best placed to take advantage.