Honest question: Lyft has just started up in my area. Uber appears to be done with the shady nonsense that dogged them at the beginning. Why do I choose Lyft over Uber?
On top of this, there isn't really much one company does that the other doesn't. Lyft line in SF is great, but I believe Uber has something similar there so it's not very unique.
That said, the biggest reasons I would support Lyft are:
1. Lyft doesn't appear to be run by immoral people. One of the reasons I would be hesitant to work at Uber and don't want Uber to monopolize the industry is that they have shown that they are willing to do shady things that hurt others to achieve their goals. I would hate to see another Comcast come to power where we are all stuck with them despite hating them. Right now Uber gets away with not being hated mostly because people paint taxi companies as even worse, but if those go away I wouldn't be shocked if Uber suddenly doesn't look like the saviour we thought it was.
2. Having competition and alternatives helps you as a consumer. If drivers find a way to game the Uber surge pricing (I read about this happening but I'm unclear how true it is) to cause fake surges then having other options for a ride means you aren't stuck paying 3x the normal fare because all the drivers shut off their Uber apps to drive up surge pricing.
You may not choose Lyft over Uber every time. You might not even choose Lyft for your next 10 rides as finding drivers in a new city may be tricky, but I would at least suggest you install both apps and give Lyft a try.
From a consumer perspective they are indistinguishable, however talking to the drivers each has a different pay structure (e.g. I think after XX rides lyft drivers keep all of their fares).
Obviously there are various sweeteners from either sides, but many of the drivers who exclusively drive for lyft formally drove for uber and said they felt better treated both by the company and the customers.
My favourite was a guy who bought his car through uber finance with the intention to drive for lyft. I'm guessing there was little love lost there.