Unreal 4 has full support for OBJs. The issue is that the file format lacks itself support for some of the nice safety features that FBX includes. If you screw up and export it with an FBX, generally you'll be okay (but his screenshot indicates significant issues that go beyond the file format). If you screw up and export it with an OBJ, those errors will become more obvious.
I prefer to export with OBJ when I'm testing meshes since it's quicker, but I switch to FBX for the final import and I use the guides in the documentation to double-check everything.
I'm willing to go along with Skanibani if he thinks he's got this (for now), but I'm going to continue being critical and post any relevant, helpful links I have so that this project can be successful, providing that he's got the effort and isn't going to cheat on it.