In Chicago and Richmond atleast the drivers I've talked to that are doing it for a full time job tend to drive Uber, Lyft and every other small start up in the area. The drivers that aren't just getting started said they use Uber for volume but will take a Lyft over Uber because of the better pay. The only drivers I've had that are Uber only are just getting started/trying it out.
The drivers I've talked to that just do it for a little extra cash overwhelmingly prefer Lyft. Most said it is because of the better pay but I've also heard more than once that Lyft customer's tend to be more well behaved in the car for whatever reason.
To be fair, this is all anecdotal and I usually prefer not making chit-chat but if the driver insist I always ask them their preference since the driver's always have an opinion that is interesting enough for the duration of the ride.