Uber actually transports people. Ford actually builds cars. Google... likes letting smart people do smart things. While Ford may be the underdog in the race, I like its chances. It has the operational experience to take a "works-in-concept" to "works-in-reality". The software part, while difficult, is not the hardest part of "TaaS". The systems part is.
While we'll see autonomous taxis operating in some capacity soon, they have to work extremely well and be profitable to justify an aggressive rollout, and that's likely more than a decade out. It's anybody's guess as to what the playing field will look like then.
Many analysts and speculators are getting ahead of themselves by conveniently ignoring just how much of the technical problems of autonomous vehicles need to be solved before these vehicles are ready to venture beyond very carefully managed services operating only in optimal conditions.