The Mummy/Scorpion King Universe: This universe has "on its team" from The Mummy and The Mummy Returns: Imhotep, Rick O'Connell, The Army of Anubis, The Scorpion King, The Mummies and the Magii. From the Scorpion King they have Mathayus, Cassandra, Memnon, and the imperial guard and/or army. The books of Amon-Ra and Horus (I can't remember if those are the names) are allowed as well, if they can do anything.
The Sky Captain and the World of Tomorrow Universe: Although this universe was only shown in one movie, there is a lot to be taken from it. First the good guys: Sky Captain and his plane, Capain Franky Cook and her aerial army, Dex and his advanced technology. The bad guys: the gigantic robots, the flying machines, the spaghetti-armed droids, and the mysterious android.
The Fight: First off, I listed Rick, the Magii, and the characters in the Scorpion King as a point of procedure but they will easily fall before the might of the fighters from the Sky Captain universe. I mean, imagine guys with swords trying to take down a 5 story tall robot, its just crazy. In this universe battle, the arena is the planet Earth divided in 2 with each half representing the landscape of the representative universe. In this case, the Mummy half is basically all desert and the Sky Captain would be the 40's style city landscape and I guess the ocean.
As always, I am breaking down the battle into simpler components. The main players from the Mummy/Scorpion King are Imhotep, his mummified priests, The Scorpion King, and the Army of Anubis. These are the only guys that I see being able to survive the robots' attacks. Imhotep can teleport away and/or around the eye beams of the tall robots. Supposedly the Scorpion King could only be killed by that staff, which leads me to think that he is invulnerable. I usually make this stupid assumption. Dex invented that disintergration ray and the robots' eye beams seem to have the same affect on matter. Energy is energy whether created by magic or science, meaning that the Scorpion King logically should be evaporated by eye beams. I usually go with my rule that uncertainity rules in favour of the defender but it is hard to rule against a disintegration ray! The mummies will fall the same way, although they will continue to come forth like they always seem to do. Imhotep is more versatile so I believe he will last against the robots. He will take out all the aerial craft with a sand storm. The armies of Anubis will take out what is left of the humans, the spaghetti-armed droids and the mysterious android. The armies of Anubis are magical and come from out of no where (I guess) so they can re-form after being blown away. But there is a catch: although they seem unbeatable, the only exist while the Scorpion King is free/alive. Since I just said that he would be taken out, this means that the army is gone as well. (Whoever kills the Scorpion King with that staff gains control of the army. I am assuming that since he will be taken out by a disintergration beam, something the magic couldn't have forseen, that the army will just disappear. So the only ones left are Imhotep and the giantic robots. If they are in the air, then Imhotep's sandstorm will blow into each other. Since I included the ocean, a tidal wave like in The Mummy Returns could take them out on land. Imhotep can evade the beams by flying around as sand. Basically I think that Imhotep has enough power to last against the robots, long enough to destroy them all. Last man standing wins.
Winner: The Mummy/Scorpion King Universe