I played Battleborn's closed beta a while back. It's pretty fun. It's a lot like a MOBA. No switching characters during the game, minions, and lane based maps. It also has a single-player/co-op mode. I've heard the multiplayer community is almost dead, so it's probably not worth getting at this point.
Overwatch is more like TF2. You have a variety of classes that can be switched to on the fly. The game modes are mostly objective based, whether it's moving carts or king of the hill. It has a large community and is incredibly fun. It's the game I prefer.