The Time Lords from Doctor Who (when they still existed) versus the Q race from Star Trek.
They've noticed each others existence and crossed realities. I'll ignore the "Doctor Who" problems with crossing into other realities solely for the purpose of these two realities crossing.
They've each decided they must have sole control over the evolution of both realities- or maybe the Time Lords decide they have to have total control and the Q aren't going to put up with that (that sounds more plausible). Both understand what they are up against and have prep time and then the war begins. No outside interference. Do the Q win? Do the Time Lords win? Do they utterly destroy each other?
Bonus scenario: The Doctor and the Q we are most familiar with (the one John de Lancie played in Star Trek) both think this war is abolutely stupid. In one of the more bizarre teamups, the Doctor and Q join forces and powers to stop this and force a truce in which each side stays out of the other's universe. Can they pull this off?