Kunoichi_Power: The advantage is mostly in the Battleboat Plus version. Current stats:

Battleboats:
White: 15017 (50.55%)
Black: 14574 (49.06%)

Dark Battleboats:
White: 28740 (54.62%)
Black: 23838 (45.31%)

Battleboats Plus:
White: 50978 (60.49%)
Black: 33227 (39.42%)

Now the important question: How do you let black take one more move in Battleboat Plus when the number of shots is determined by how may ships they have left?

(NOTE: Best thing in my opinion is to do is make sure you play 2-games, switched colors when you play)