When I was in Colorado Springs, Lyft was much more available than Uber so I used it for the first time after only having ever used Uber for the past year.
The major thing I found different was the driver wanted me to sit in the front and was much more enthusiastic about conversation. It wasn't bad but it was definitely different and somewhat offputting. Not sure if that was just a single event, but I wonder if each company encourages those differences in driver interaction.