Catman

They both have a different kind of art and are about cats who cause problems or mischief in the city.  

The tale of an anthropomorphic animal and its problems with society that are communicated to the audience. 

The protagonists are punk-ish anthropomorphic cats that frequently get into fights. Both are also ONAs with character designs atypical for anime. 

Short anime about anthropomorphised animals. Both have simplistic animation/artystyle, but are intended for adult audience with their content. 

Short flash-animated series about cool white cat guys. 

Both have the same shortness to them (2 to 5 minutes each) and both deal with strange philosophies. ...Or something like that.  

Both deal with anthropomorphic cats who deal with (very) unusual circumstances.