More people will use ride services when they are cheaper. Rides are a commodity. You will get there just as much with Uber as with Lyft. It doesn't make that big of a difference to most people. It's like the level of luxury in a car. I'm sure it's rare to find people not taking a Lyft or an Uber because the car didn't have leather seats.
I'm a daily user (to and from work, carless for over 18 months now) and I use the cheapest option. Historically it was Uber. Checked and for the past 4 months or so, it's be Lyft so I switched. Now it's back to Uber because of one reason, price.
The drivers on Lyft seem a bit happier and nicer but, it doesn't really make that much of a difference. I'm not using a car service for the quality of a 10 minute conversation with a random stranger that I'll never see again.