The outcome of a fight between an alligator and an elephant would greatly depend on the situation, the environment and the physical standards of each animal. A series of trials would have to be run to determine the outcome percentage, but neither animal is likely to win every time.
While elephants have a large size advantage, incredible tusks and stomping power, they are clumsier and less adept at fighting than alligators. Alligators are carnivorous and have many sharp teeth that are made for killing. Elephants, on the other hand, only have defensive weapons because they eat plants and not meat.