Okay, I know "now" is a couple months out-of-date, but I didn't know this until today, so I figured some other people might not either.

I have both OsmAnd and CoMaps, and I generally prefer OsmAnd for its extensive customizability, Carto render, and the fact it can be kept more up-to-date. So it surprised me it didn't have the option to view 3D buildings, since OSM for a long time now has kept track of information like building levels (building:levels), height (height), and even building parts with varying levels and heights. OsmAnd introduced this with Version 5.3 on April 21 for Android and April 24 for iOS.

Note that there are many towns and cities where this data either doesn't exist yet or is incomplete, but even then, buildings will default to building:levels=1 in terms of the heightmap, so it'll still give you some "texture", so to speak (and show where you can personally improve the map if you contribute).

This was one of the few things on OsmAnd I was really missing from CoMaps, so it's great to see it!

Edit: Looks like there's a "level of detail" suboption for building part levels, i.e. where different parts of the same building can have different levels.