Originally Posted by voxsartoria
I'm pretty sure they cannot mate.
No, they can mate and produce offspring. It has happened at at least one reptile park or farm. Interesting because they are separated by some 80 million years of evolution. Although croc-like reptiles go way back into the Triassic, the true modern-type crocodiles and alligatorines, which include the caims) date "only" from about 80 million years ago.
As to which would win in a fight, most likely the crocodile. They tend to have more aggressive temperaments than gators, at least the larger species.
Of the 23 (I think) species of crocs and gators, two--the Salt Water Crocodile and the Nile Crocodile--are highly dangerous man-eaters. Five other species are occasionally or potentially dangerous--American Alligator, American Crocodile, Orinoco Crocodile, Black Caiman and Indian Mugger. The remaining species are not particularly dangerous to adult humans.