Anti-heroes vs Villains
Anti-Heroes/Anti-Villains and standard villains generally only end up on the same side at times because they are both opposed by true heroes. There is a strong likelihood though that in the absence of heroes, the two groups would not really get along.
So when the world wakes up one morning to all the heroes gone, and these anti-heroes and anti-villains find themselves in a world ruled by true, crazy, destruction-craving villains, they are forced into a position of opposition because, if the villains rule, then everything these others hold dear, be it money, power, safety for their people, or guarantees for their future, all of it is in danger.