I've had drivers in a couple of different cities tell me they're on both apps, but there are generally more fares on Uber, since it's a more famous brand.

In some cities, the base fares are notably higher on Lyft, too, making more money for the drivers but driving more customers to Uber. I'm not sure about other apps (Sidecar, etc.).

But basically, the drivers can get a cheap fare fast on Uber, or they can wait longer to get a slightly better fare on Lyft.