Buses on dedicated lanes have found to be cheaper and as fast as subways in some cities. But they're not as prestigious and it's harder to ensure that the next government won't destroy the system by opening it up for other vehicles.

Trains make sense for longer distances (more efficient) but in cities, buses work as well and can be used more flexibly.

That's not entirely what public transport companies have found. Busses don't scale as well as using entire trains. I have seen a bus route replaced by a tram, because they had to send double-length busses at every few minutes. Which in practice meant that you would see two or three of those busses arrive at the same time. A well-planned public transport system will use a mix of busses of diverse sizes in conjunction with trains/trams for trunk routes.

The big problem with fully segregated bus lanes vs subways is that they have a lower peak capacity. However, this Boring company thing has a peak described capacity of only 2k/hour, lower than even a BRT/segregated lane bus system. Real subways have far higher capacities, obviously.

There are reasons for trains over buses (like increased capacity and lower dwell time), but neither of those are important to the system that Musk is envisioning.