There are several possible strategies here. Some teams play the odds. For example, there are far more contestants in the rib category at most competitions than there are for whole hogs, so statistically, at least, you have a better shot winning in whole hog than in any other category. Of course, it takes a lot of experience and know-how to nail the perfect hog.
Other teams go for shock value. Most barbecue contests have an “Anything But” category in which you can enter any dish save one of the big three (ribs, shoulders, or whole hog). Perhaps you have a killer smoke-roasted pecan pie, or nobody barbecues alligator like you do. Chances are there won’t be a lot of direct competition in these categories. Thus, you improve your chances for winning.