From my experience in NYC many drivers drive for both Uber and Lyft. In an anecdotal poll I ran with those drivers, they say Uber riders usually like to be left alone while Lyft riders are more chatty.
In NYC drivers may times work with both companies.
My backseat survey had most drivers say Lyft riders tend to be more chatty and friendly, while Uber riders tend to be busy with their phone and not say much.