Indirect ToF: easier to manufacture in small form factors, relatively cheap, well established technology. Easier temperature calibration and lower precision required when manufacturing the emitter, meaning cheaper components and more vendors that can make them. Because the technology can only measure the shift in phase, there is phase ambiguity between waves. The way this is dealt with is to emit multiple frequencies and use the phase shifts from each to disambiguate, but you usually only get a few channels so there ends up being a maximum range, after which there is ambiguity (aliasing, if you will) about if an object falls in a near interval or a far one. Multipath can commonly also cause such artifacts in indirect ToF systems. Finally, because they are continuous wave systems, they can (though modern indirect ToFs try to mitigate this) interfere with each other like crazy if you have multiple running in the same area. I’ll note that there are also gated systems that I would characterize as indirect ToF, that use a train of pulses and an ultrafast shutter to measure distance by how much of each pulse is blocked by the shutter. These suffer from more classical multipath (concave regions are pushed away from the camera), and are not very popular these days. You are right to call out that Microsoft is very heavily patented in the ToF space, and they ship probably the best indirect ToF you can buy for money on the HoloLens 2 and Microsoft Kinect for Azure.

Direct ToF is a newer technology in the mobile space, because it has proven challenging to miniaturize SPADs, which are really the core technology enabling them. Additionally, the timing required is extremely precise, and there are not that many vendors who can supply components adequate for these systems. While there are patent advantages, there are also some significant technical advantages. Direct ToF systems have better long range performance, are much less affected by multipath, interference with other devices is minimal, and most critically - you can push a lot more power, because you emit a single burst instead of a continuous wave. This is really important for range and SNR, because all active IR imaging systems are limited by eye safety. For eye safety you care about not just instantaneous power but also energy delivered to the retina over time. Its helpful to recall that for all these active IR systems that go to consumers, they need to be safe after they’ve been run over by a car, dropped in a pool, shoved into a toddlers eye socket, etc - so this puts pretty strong limits on the amount of power they can deliver (and thus ultimately on range and accuracy). Direct ToFs are also really nice thermally, because your module has a chance to dissipate some heat before you fire it again (vs CW systems where you’re firing it a much higher fraction of the time).

Kudos on the explanation. I'd love to see you do a blog pot that elaborates on these different methods with diagrams for laymen like me who find this fascinating.