Uber's been likely working on self-driving cars, potentially in partnership with Google. What Tesla has as an advantage though, is an assembly line to produce lots of quality cars. In other words, Tesla will likely be ready for the future of transportation before Uber.
Also millions of miles of fleet learning a day, which Uber doesn't have, since they don't own the cars. Self-driving cars is a supervised learning problem, and he who has the data wins
Tesla's other advantage is a global fleet that is actively logging millions of real-world miles a day. I don't think that can be understated at this stage.
But with Tesla's open policies, such as open sourcing all their patents, maybe they will happily supply Uber with all the self driving cars Uber might want, plus the API's to remotely control them?
I also think that Tesla will have an easier time acquiring top talent in both the autonomy software and manufacturing. Uber/Google have to partner with Old Guard automotive companies.