I'd say that Uber/Lyft would be better positioned to take advantage of driverless vehicles. The hard part is the tech, personal for fleet management is a cost center. They have already mastered outsourcing low-skill cost center type jobs to large numbers of poorly paid contractors. And both companies have business relationships with fleet management companies.

So once either company successfully develops proprietary IP that enables fully autonomous cars they should have a clear road to profitably. They can use their existing relationships with fleet management companies to handle that part. And that is a mature industry, so the presence of a lot of capable competitors will keep costs down for Uber/Lyft. If they do need to do a bunch of hiring for new low-skill positions they can probably outsource it easily. I think the major winners will be tech companies and car makers. I don't think the fleet management industry will capture the majority of the profits, but they will probably get a minor portion.