I'm going with the monkey in pretty much any battle that you could stage between these two:
Battle of wits? Grape Ape was WAY more eloquent than the Caveman
Battle of fashion? (shut up, I'm a girl, we think about these things) While a too-small jersey-esque bolero and a bowtie isn't the first choice of most fasnionistas, it definitely beats that ratty old cape.
Cage match? Hello, giant freaking gorilla versus little wookie with 8 fingers - no match up at all.
Not that it would matter all that much to cavey since, at the end of the day, he went home with how many girls?