From my limited experience (doing Amethyst's Pong tutorial and glancing through Bevy's home page), Amethyst is more mature and also seems more complex (and presumably more powerful). There's quite a bit of boilerplate to get started, but it gives you very fine-grained control over everything like how assets are loaded, how components are laid out in memory, etc. It seems like it's aiming more for the "real game studio" market than for enthusiasts, although last I checked it's also mainly focused on 2D for the time being.