Depends on the fight. If it's wrestling I'd take him - I have him on size.
If it's boxing I don't know - if I landed a haymaker I could light him up, but he's one of those tall, fast skinny guys and could just wear me down and then POOF! turn out the lights on me.
If it was a footrace I think Omaha would have time for a beer before I got within sight of the finish line.
If it's tiddlywinks I would totally pwn him. I am the Master of Winks.
Spelling bee? I don't know, but I'm a pretty good speller. I can't seem to remember Omaha having too many spelling errors though. That could end up being a test of endurance.
If it came down to a slap-fight, I think ET would win. He has giant hands compare to Yoda. That said, this is not a slap fight and ET is pretty useless.