The Queen’s Bishop Attack is basically the trompowsky where black hasn’t played Nf6 yet. It’s an oddball dramatic grab- playing Bg5 on move 2- the bishop hanging there in space pinning nothing and threatening nothing. James Plaskett has written a book on the subject, that is basically a game collection targeted at beginners in the “Batsford Chess Revealed” series of books. However, I have had several masters tell me that this book contains nuggets of knowledge that are far more complicated than most beginner books aim for. In particular, there is a discuss of the following type of position:
Here we see the two queen’s staring at one another across the board, putting the question back and forth. When to take and whether to take is often something even masters may bicker over. The following game demonstrates a straightforward idea for using the queenside space gained in the opening to generate pressure against a single weak point in order to generate a breakthrough using this theme. When i was a weaker fish than I am now, I almost always took my opponent’s queen when I had the black pieces and was offered this option. As I got stronger my opinion flipped one hundred and eighty degrees, and I thought that one should never take the queen allowing white a free hand on the a-file and queenside pressure. Now I appreciate that what is happening on the rest of the board matters as well, however, in the following example I think we can agree that black would have done better to not have taken white’s queen. In any case, these positions are incredibly common in off-beat queen’s pawn games such as the tromp, torre, and Queen’s Bishop Attack, so a careful study of the position is necessary before jumping to any quick conclusions about these positions in general.
In essence, I think that capturing the queen and doubling the opponent’s pawns is a risky and double edged idea. You have to be prepared for the coming presure and aware of what weak squares will need to be held before lashing out with the Queen exchange.