I think there's likely to end up being a third option: Public transport with self-driving cars for last mile at each end. That way you have the convenience of door-to-door, combined with the efficiency of mass transit for the bulk of traffic.

There are also other advantages, like it expands the effective catchment area of stations, making them more viable even at lower densities. And the cars themselves can be much smaller and more efficient as well, since they don't need the range, and they don't need to be as comfortable if people are only sitting in them for ~5mins.