Disclaimer : I live in Berlin and work in IT.

The benefit that Uber gives me here in Berlin, for me, is really big :

1) Global usage ( I travel a lot around Europe and I can use the same app everywhere, no need to look for a local app )

2) Using app that is potentially / economically better. I certainly expect less bugs than the other apps.

3) All english user interface for every country I go to and pay using the same credit card.

4) Rating drivers

So ... IMHO The big potential of Uber is that it tries to solve the taxi problem everywhere. Just like booking.com for the whole world.

Competitor solution for this problem is MyTaxi. It is popular in Berlin and I also used it in Lisbon last week.