Our use case for After Effects was video stabilization. We have had good luck with Blender for this. I've also noticed that the old simple motion graphics I used to do - title overlays, etc - Blender can do easily. As for more intensive motion graphics, I can't speak too much to that.
As for any After Effects-style NLE capabilities - DaVinci Resolve knocks those out of the park. You'll also probably hear a lot of people singing the praises of Natron for NLE and Motion Graphics, and from our experience with that it seemed like the learning curve was non-trivial, but anything AE (and some aspects of Premiere Pro) could do, it could match... Good luck!
As for any After Effects-style NLE capabilities - DaVinci Resolve knocks those out of the park. You'll also probably hear a lot of people singing the praises of Natron for NLE and Motion Graphics, and from our experience with that it seemed like the learning curve was non-trivial, but anything AE (and some aspects of Premiere Pro) could do, it could match... Good luck!