I'm no FM, but here's how I would look at it logically, while keeping in mind that calculation can overrule logic.

Black's move pretty much must be a check, given the mate threat and the threat to Black's queen. Three of the checks look really bad because they immediately lose the queen for no discernible benefit. This leaves only two choices: ...Bg4+ and ...Qxc2+.

While ...Bg4+ puts the bishop en prise, it is easy to see (a two-ply calculation) that taking it would be disastrous for White, even though, according to the engine, it is White's best move! If White doesn't take, even without doing a lot of calculation, you can have a "feeling" that there are mating chances now that you have your bishop and queen cooperating in the attack and the possibility of adding the other bishop.

With ...Qxc2+, the problem is that the only attacking piece is the queen, which on its own gives you perpetual check at best. Now that your queen isn't pinning White's rook against the queen, there is no good way of bringing the light-square bishop into the attack.

The problem is that if it so happened that ...Bg4+ didn't work after all (something which you can't know for sure without further calculation), it could well be that a draw is the best result for Black, which would make ...Qxc2+ the better choice! So "logic" can give you an indication of which move is likely to be better, but it is not foolproof. How much a FM would calculate probably depends on how much time they have. I would be interesting to hear from an actual FM. :-)

I'm no FM, but here's how I would look at it logically, while keeping in mind that calculation can overrule logic.

Black's move pretty much must be a check, given the mate threat and the threat to Black's queen. Four of the checks look really bad because they immediately lose the queen for no discernible benefit. This leaves only two choices: ...Bg4+ and ...Qxc2+.

While ...Bg4+ puts the bishop en prise, it is easy to see (a two-ply calculation) that taking it would be disastrous for White, even though, according to the engine, it is White's best move! If White doesn't take, even without doing a lot of calculation, you can have a "feeling" that there are mating chances now that you have your bishop and queen cooperating in the attack and the possibility of adding the other bishop, as well as the rook, which is now free to move to the open file.

With ...Qxc2+, the problem is that the only attacking piece is the queen, which on its own gives you perpetual check at best. Now that your queen isn't pinning White's rook against the queen, there is no good way of bringing the light-square bishop into the attack.

The problem is that if it so happened that ...Bg4+ didn't work after all (something which you can't know for sure without further calculation), it could well be that a draw is the best result for Black, which would make ...Qxc2+ the better choice! So "logic" can give you an indication of which move is likely to be better, but it is not foolproof. How much a FM would calculate probably depends on how much time they have. I would be interesting to hear from an actual FM. :-)