Doomsday and Darkseid, both very powerful villains, have clashed before, proving who would win the battle: Doomsday. This fight occurs in the 1994 comic mini series "Superman/Doomsday: Hunter/Prey."
In the comic, a salvage vessel finds and awakens Doomsday, quite by accident, while travelling through space and surveying asteroids for resources. After he slaughters the vessel's entire crew, Doomsday finds himself landing on Darkseid's home planet. Even the power of Darkseid's dreaded omega beams, emanating from the Tower of Rage, could not stop Doomsday. Doomsday won the battle because he could adapt to defeat any opponent - that's what he was created to do.