Batman vs. Daredevil
My pick: Daredevil. The two are even in fighting skill, but Daredevil’s heightened senses give him an edge.
Superman vs. the Hulk
My pick: Very tough to say. The Hulk is powerful enough to go toe-to-toe with Superman physically, and could probably withstand the hottest heat beam he could put out. I’m going with the Hulk, mostly because he gets exponentially stronger and heals faster when enraged, and Superman apparently does not.
Doomsday vs. The Destroyer
My pick: The Destroyer, but it would be a truly EPIC battle. The ultimate mystical weapon against the ultimate genetic creation. The Destroyer’s disintegration beam would not be as decisive as some might think, since he can’t fire it at will. He has to close his visor and wait for the energy to build. Doomsday would figure this out, for sure. Not only that, but it was shown that even if you cut part of Doomsday off, he can simply reattach the piece and keep going.