None of the above.
Burms eat mainly mammals and birds. Alligators eat mainly fish and turtles--a point people tend to forget. Burms do not hunt in the water, usually--Alligators do. While burms would probably take some gators, more gators will eat burms--they'll make a nice food source for the gators, because they're not very fast on land OR water.
The alligator is supremely adapted to the Everglades, and it already eats snakes, albeit smaller ones. Because they are not direct competitors, but are fully capable of preying on each other, I see no reason why they won't both 'win'.
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