We've eaten at both, stayed at AKL and ate Breakfast and Dinner at Boma just last week. If it's for the adults BOMA is the best best, food is great with just enough ethnic items to try. AKL is an amazing resort and fun to visit if you've never seen it.
Chef Mickey's food is typical breakfast, nothing terribly unique, but great character interaction. It's also fun to ride the monorail if you've never done that before either.
Based on food only, I choose Boma.