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In the Slav, after 1. d4 d5 2. c4 c6 3. Nf3 Nf6 :

What are all the differences between 4. Qc2 and 4. Qb3 ?

Which one of them is better to reach some Catalan type positions?

Which one of them tends to lead (on average) to the most solid, quiet, positional, slow, safe and strategic positions (i.e. the least sharp and tactical positions) ?

Is one of the two objectively stronger than the other?

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I have made some research and here is what I've found:

If Black plays 4...dxc4 then they transpose (except if White is crazy enough to try the rare gambit 4. Qc2 dxc4 5. e4 but I'm never going to play this anyway).

Against 4. Qc2 Black often plays 4...g6, while against 4. Qb3 the move 4...g6 seems to be less popular.

If Black plays 4...e6, maybe it makes a difference if the Queen is on c2 or on b3. Not sure.

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    You get the most solid, quiet, positional, slow, safe and strategic positions against the Slav if you play the Exchange Slav, which isn't so bad theoretically anyway. – BlindKungFuMaster May 23 '15 at 12:11
  • @BlindKungFuMaster: Could you clarify what "not so bad theoretically" means precisely? Does it mean that the Exchange Slav gives Black equality but it's "not so bad" for White because it at least doesn't give Black an advantage? Or does it mean that White still has a significant advantage in the Exchange Slav? – Fate May 23 '15 at 12:50
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    I think today there are no significant advantages to be found for white, no matter where you look. But the Exchange Slav isn't easy equality for black by any means. Even a 2800 player can still go down against it … chessgames.com/perl/chessgame?gid=1687266 – BlindKungFuMaster May 23 '15 at 13:19
  • Or an almost 2800 player (at the time), another recent game I remember: chessgames.com/perl/chessgame?gid=1699939 – BlindKungFuMaster May 23 '15 at 13:24
  • @BlindKungFuMaster: But I see that in both of those two games White played the Nc3 Exchange Slav. I start with 1. Nf3, not 1. d4, so if I play the Exchange it will be the Nf3 Exchange: 1. Nf3 d5 2. d4 Nf6 3. c4 c6 4. cxd5 cxd5 5. Nc3 Nc6 6. Bf4 Is this variation of the Exchange Slav also very popular at the GM level? Or is it regarded as inferior to the Nc3 Exchange Slav? – Fate May 24 '15 at 13:06
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After quickly looking at the differences, I think Qb3 is more suited if you want to fianchetto.

The queen puts pressure on b7 and d5 and combines nicely with a fianchettoed king bishop.

If the queen is on c2 black often plays g6, planning to fianchetto and also play Bf5 with tempo.

Both moves are equaly popular. The choice is yours!

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The difference is that Qc2 will allow you to later push the b pawn at the expense of you pressuring the black b7 pawn. With the Queen on c2 you also gain the option of combining the Qc2 and Bd3 against the h7 pawn later when the black King is castle. I recommend delaying the Queen move until later. Develop your pieces and castle first.

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