What are the cases in which is good to take Qb3 in "London System'sSH" setups and why

Question

I know that the main idea against London System is to play Qb6 to attack the b2 pawn which is unprotected due to the early Bf4 white plays (generally) at move 2. Normally white reacts to the threat with Qb3, covering the attack of the queen on b2:

[Title "London System setup"]
[fen "rnb1kb1r/pp2pppp/1q3n2/2pp4/3P1B2/1QP1P3/PP3PPP/RN2KBNR b - - 0 1"]

I also know that taking the queen here is considered not a great idea for black... This is due to the great activity white's rook on a1 would gain after axb3.

In this position instead (reached from the Queen's gambit declined opening), Qxb6 is considered the best move for white by Stockfish...:

[Title "QGD setup"]
[fen "rn2r1k1/pp2bppp/1qp2n2/3p3b/3P1B2/1QNBP2P/PP2NPP1/R4RK1 b - - 0 1"]

Someone could please explain me what is the rationale behind this? Why in a case taking the queen (and so allowing great activity of the rook on the open file) works and in the other case doesn't? And, in the case it doesn't work, what should be the right plan to follow?

Answer 1

The answer is very simple and can be summed up in one word - "development".

In the first position it is essentially a "Mexican standoff". If either side plays QxQ they hand the advantage to their opponent. This is because the combination of half open 'a' file, resulting pinned 'a' pawn and battering ram 'b' pawn are very difficult to deal with and the opposing side gets very easy development and attacking chances. For example:

[Title "London System setup"]
[fen "rnb1kb1r/pp2pppp/1q3n2/2pp4/3P1B2/1QP1P3/PP3PPP/RN2KBNR b - - 0 1"]

1...Qxb3 2. axb3 cxd4 {probably best} (2...Nc6 {retaining the tension} 3. Nf3  e6 4. Na3 Bd7 5. Nb5 Rc8 6. Bd3 a6 7. Nd6 Bxd6 8. Bxd6 cxd4 9. exd4) 3. exd4 Nc6 4. b4 Bf5 5. Nf3 e6 6. b5 Nd8 7. Nbd2

In the second position with both sides close to completing their development this does not apply. The rooks are at most one move from being connected and the half open a file is much less of an issue because the opposing a pawn is not pinned. Furthermore the doubled white b pawns are going to be isolated and a liability in an endgame. Note they cannot be easily eliminated by advancing because black can play Nbd7 and a6 when there will be 2 black pawns guarding the b5 square. In any case just playing b4 is difficult for white. For example:

[Title "QGD setup"]
[fen "rn2r1k1/pp2bppp/1qp2n2/3p3b/3P1B2/1QNBP2P/PP2NPP1/R4RK1 b - - 0 1"]

1...Qxb3 2. axb3 Nbd7 3. Ng3 Bg6