I always noticed people on the net like to label Zidane a monkey..I never quite got this. I know it's said in the game I think but that's about it.
Did Zidane seem like a monkey to you? His constant "attack mode" stance doesn't seem very monkeyish to me. Always made me think of a cat ready to pounce.

Also, the feathers in Kuja's hair, many seem to think they are actually part of his head considering they stay when he goes Trance. To me, I always got the picture of some kinda bird when I looked at Trance Kuja's hair.

have you not noticed his tail? though it's more associated with a gibbon or lemur but the monkey association is there. But a Terran with a tail is just a genetic feature they once had.

I think it depends on his attitude at the time. While he's joking around, Zidane is comparable to a monkey as he, for a lack of better words, monkeys around. Deflated or upset, he's like a dog with his tail in between his legs. I agree that while in battle, he's like a cat ready to pounce.

Kuja's bird-like affiliation probably comes from his elegance and grace.