Just because two anime characters fall on the villainous side doesn't mean they get along. In fact, many shows feature anime villains fighting each other, a situation that, in theory, should work out for you the viewer.
Two anime villains may beef over personal grudges, like the one the ambiguously villainous Sasuke Uchiha of Naruto holds for the explicitly villainous Danzō Shimura; villains like Greed from Fullmetal Alchemist deciding to show some heroism at the last moment; or even groups like Ladd Russo's gang from Baccano! saving people from a cult because they want to be the ones who slay those people. They may not be final anime fights, but villain vs. villain battles in anime come extremely close to matching the hype.
Villain vs. villain anime fights offer some of the most exciting brawls the anime world has to offer. Neither side operates with heroic intentions in mind, and they often won't hesitate to commit horrifically evil acts in the process. With no heroes around, all bets are off and the drama hits a new high.