Do these ride-sharing companies even have quality metrics in any meaningful sense? Surely the quality of service you receive is a function of the individual driver-subcontractor, not of whatever mobile app you happened to hail them from?
I took a Lyft recently from a driver who had an excellent rating. He happened to also be an UberX driver and confessed he had almost been kicked out of Uber because he was getting bad ratings. All his feedback was along the lines of "driver is too chatty, tries to make unnecessary conversation". With Lyft, the whole point is that your driver is friendly and makes conversation.
Uber drivers seem to be strongly encouraged to offer water and gum where only the occasional Lyft will have either.
There are a couple other small differences but yes, drivers and passengers select which community they want to be a part of. Depending on which aspects of each you prefer, the qualities definitely differ.