I switched over to only using Lyft, but like the OP states, if Waymo came out tomorrow I'd probably switch to that.
This goes for other markets as well, it's just generally hard to get good information.
If you’re in a market where they operate, I can heartily recommend it.
Thus the drivers won't care which app is running, since they will be making (more or less) the same $$$$$. All they need it to do is ensure they are driving people around/keeping busy, and if one company is bleeding customers, they will simple start 'the other app' and continue driving.
I may be oversimplifying the above, but it's the general idea/practice.
As Uber Probes Sexual Harassment At Its Offices, It Overlooks Hundreds Of Thousands Of Female Drivers
On Lyft in the same cities, I always get a much more oddball mix of vehicles, with much more diverse conversation from the driver. I've had biotech founders looking to recruit and make beer money pick me up on Lyft rides going from the South Bay to the SF in the Bay Area, real estate agents and recruiters drive me in many cities, and many others that are clearly doing Lyft as a side gig rather than a profession. On the downside, this usually means that they're less aggressive drivers in terms of optimizing for speed and route efficiency, but it can make for a more interesting ride and better chitchat along the way.
As a result, I almost always default to Lyft unless there's a huge price spread in Uber's favor.