Qe2 vs Qc2 in the Queens'

A. In general why done one choose Qe2 or Qc2  over the other in the QGD?

B. In the specific line: 1. d4 d5 2. c4 e6 3. Nc3 Nf6 4. Nf3 c6 5. e3 Nbd7 6. Bd3 dxc4 7. Bxc4 b5  8. Bd3 Bb7 9. 0-0 a6 why is10.  Qe2 sometimes played (15x according to chessgames.com database) but never 10. Qc2?

C. d4 d5   2. c4 e6   3. Nc3 Nf6   4. Bg5 Be7   5. Nf3 O-O   6. e3 Nbd7  
7. Qc2 is sometimes played. Qe2 is never played. Why?

Thanks for your thoughts and time.

It depends on what you want to do with your Queen.

In the first example, the Q goes to e2 mainly (I think) to get it out of the way of the retreating Bishop, which may come in handy and needs a retreat square/diagonal. If Black plays a c5 break with a Q on c2, the Knight might go to c5 and pop the Bishop.

In the second example, the Q is heading to a more active file with the intention of pressuring the Q-side. Moving Qc2 so early may not be the best idea either. But it makes sense. Qe2 would  be pretty passive in this position.

In example C, Qe2 would block the light-squared bishop, which is already developed in example B. This would suggest that e2 is generally a "better" square for the queen in terms of the e4 pawn push, but not so much better that c2 wouldn't be a good alternative if the light-squared bishop is still undeveloped. In addition, there are other good avenues of attack unique to both squares that must be considered (attacking the pawns on c7 and h7 vs. securing the e5 square), and these depend on the positioning of the other pieces - in example C, black's c-pawn is still dormant, while in example B, black has no d-pawn to stop white's e-pawn push.

Thanks guys. Some useful stuff for me for sure.

Also the queen of c2 is more poorly placed as black intends RC8 which would be on the same file as the queen forcing the queen to move again. Also the bishop on b7 is looking at F3