The alligator's wide snout is good for handling it's wide variety of food. Alligators rely on their stealth and power to take down their prey. In contrast the slender-snouted croc relies more on speed than strength and a thinner snout cuts through the air a lot faster. This thinning of the snout is taken to an extreme with the Indian gharial (Gavialis gangeticus) which has a snout so thin that it gives the animal a very strange appearance. Gharials, being only fish eaters need the thinnest possible snouts in order to cut through the fast moving water to grab it's fish.
As one can see, each crocodylian has its own custom tailored snout to deal with its food requirements.