WARNING
Spoilers
If these two individuals should reach hostility with each other for some reason and meet on a battlefield that can support both of them as they appear in their respective games, then who would win?
Mehrunes Dagon is a giant Goro from Mortal Kombat with a huge double axe in his upper right hand and Wolverine claws in his lower left hand. The other two hands punch. If he were to left hook Liberty Prime's head with his godly upper left fist then will it may well pop off like a champagne cork and be sent rolling on the ground. But it would matter very much whether the punch strength was brute force or magic might. Either way, it would be best for him to give priority to his axe instead. Mehrunes Dagon is a major god, and the wiki states that he cannot be killed by a mortal. In Oblivion http://www.youtube.com/watch?v=qOYUYhbMkVs and lost when he was bitten in the neck and spitfired by the dragon. I would think that these flames are mystic fire that are is much hotter than the fire that we know. MD could be in trouble against Prime's beam. Fortunately, Dagon has an energy projectile that might be useful against LP.
Liberty Prime is the Iron Giant. He does not count as a mortal by any biological sense. He does not 'think' like us, he assesses his situation and reacts by the tactics of his programming. As mentioned, he has a beam that is powerful enough to wipe vertibirds out of their flight and dismantle them into small debris while they are still airborne. Dagon would need to shoot and hit first or he may be hurt if the beam is powerful enough. Prime also has a morale breaker in the form of language, which is a pile of wrongheaded, ugly propaganda about how people deserve freedom. But Prime's assets are many. I've seen him overload Enclave barriers by touching them, throw heavy objects and his custom bombs like a grenadier, wipe out multiple targets with his secondary mini-beam, and punch a wide hole into a fortified building. http://www.youtube.com/watch?v=ZobDf3XkiJM.
I think Prime has a fair chance since Dagon has previously demonstrated that his godly power is not unlimited. Then again, Dagon is associated with the disasters of fire, earthquakes, and floods and I didn't consider these cases because I haven't seen them in game. Now that we have been reacquainted with these masters of destruction, how do you think the battle would proceed and who would prevail as champion?