Repeaters and max hangs target different parts of the strength training cycle, so yeah as folks are saying it depends. The standard cycle is transition -> hypertrophy -> max strength/recruitment -> ME; as TFTNA says, you can skip hypertrophy if you’re not trying to absolutely maximize strength in a given muscle (as Scott J is always saying, alpinists don’t need to squat 4x body weight). Repeaters target hypertrophy, and though I once thought otherwise, there is really no kind of climbing that can mimic the intensity of an hour-long focused repeater session. Developing new muscle fibers lays the foundation for long term progression in strength, whereas recruitment works only on the muscle that’s already there — max hangs for sure work very well, especially for people that are newer to finger strength training, but they have a lower ceiling.
The tradeoff is that repeater phases are vastly more exhausting than max hangs, so you really have to budget in a month of not climbing much of anything challenging for you. That’s only worthwhile if you’re sure you’re failing on your goal routes because you’re not strong enough, rather than a lack of technique.
Addressing some specific points — the anderson bros recommend only training hypertrophy (repeaters) on the hb because it’s easy to train max strength (recruitment) with campus board or limit bouldering, both of which also help with technique. The hb doesn’t have a technique component. You can train max strength just fine on a hb, as well, but then you’d be spending two phases on a hb (there’s really no way to target hypertrophy with climbing, so that has to be on the hb). Also my understanding is that the lopez study tested how much the hb routines improved recruitment, so… not super informative that the routine that actually trains recruitment would do better — repeaters are for hypertrophy, not recruitment.
I do agree that comparing-against-other-methods was a weak point in the anderson bros book + blog (i guess they were being polite?), but luckily there’s waaaaay more detail in old threads in their forums.