I wonder if you used Lyft a long time ago, because I don't even notice the tip screen until next day sometimes. When I leave the car, my phone is in my pocket, or I'm already doing something else on it, so I do not see the tip screen until I happen to open the app next time. Dismissing the tip screen is a single tap with or without leaving a tip, so it's never been a usability concern for me.
I'd rather take care of the tip right away (or as soon as I have a chance) than have to remember to do it well after the fact, but in either case I'd much prefer to not have to remember it at all and just be done with the whole thing the second I step out the car. (There's also the rating thing with both Uber and Lyft, but at least that's faster and I wouldn't really feel bad if I were to forget about it.)
That, and as I sort of implied earlier the honesty/inclusiveness of the fare estimates is a concern, in that whereas a $10 estimate in Uber means exactly what it says with Lyft I have to remember to do some additional math on top of that.
(These probably sound like the epitome of "first world problems"; I'm not saying that Lyft isn't good, or even that it's dramatically worse than Uber for me — just that their competitive landscape is such that even minor usability issues like these are currently costing them my business.)
I usually use Lyft, and one reason is that I get the option to tip the driver.
I like Lyft's model where the driver doesn't know how much you tipped, but knows how much in tips he gets at the end of the day in aggregate... it reinforces positive service while removing any friction to tip or not.
If Uber is going to implicitly make tipping a requirement to not feel like a jerk (as with Lyft), but without copying Lyft's ability to tip from the app, suddenly Lyft looks a lot less unattractive by comparison. Now that I know this is starting to become a concern at all, I would switch to Lyft immediately if they just added a setting for a default auto-tip that would be factored into fare estimates.
I really don't understand this aggressive, cutthroat effort to compete on price at the expense of their drivers; I can't be in the minority in considering price a secondary concern to the overall UX, so long as it isn't unreasonably inflated like taxi fares. Is it possible that the underlying model of ridesharing isn't actually particularly more efficient than the taxi industry, and that Uber/Lyft rates will naturally converge with taxi rates over time as they gradually stop subsidising rides and/or underpaying drivers?