So I take it that we are going to ignore the mate in 3 here and we imagine pieces and positions around this structure.
The answer to your question varies by position. It really does depend on the structure of the position. For instance, is the a1-h8 diagonal open? There may be tactics involved with Bxg7 and then Qd4+.
Sometimes black will take on h6 if it deflects the queen away from something useful on the queenside.
There is not really a fast and easy answer to your question.
I have a question about mid games in general and I was wondering if someone could help me out. In the position, I only show the pieces that are important to my question. NOTE: The white king's location is unimportant.
I find positions in games in which the pieces are used just like in the sequence I show. However, I think that after white plays Bh6, black should ignore the bishop and play something unrelated (develop a piece, push a pawn, etc.). Later, white plays Bxg7 and black plays Kxg7 and avoids having white's queen so close to the black king.
So why, whenever I see a game that reaches this type of position, black plays Bxh6 instead of my suggestion, which to me seems better? Anyone know?