In the Queen's Gambit Declined, after 1. d4 d5 2. c4 e6, what is the difference between playing 3. Nc3 and 3. Nf3? Here are Chessbase's statistics after 1. d4 d5 2. c4 e6 :



Nc3 - N=116,000 - W=58.2% - Av=2152 - Perf=2176


Nf3 - N=54,000 - W=60.3% - Av=2239 - Perf=2264



.


N = The number of games played
W = White's score in %
Av = The average rating of players playing White
Perf = The average performance rating of players playing White


.

So clearly 3. Nc3 is two times more popular than 3. Nf3. But 3. Nf3 has a better score (though if we calculate Perf minus Av we find +24 for 3. Nc3 and +25 for 3. Nf3, which is pretty close).

.

There are four things you should know:

Firstly, I am an extremely positional player, I don't like sharp and crazy games full of tactics. I would prefer the move which in average leads to the most solid, positional, slow, closed, strategic and quiet positions. I don't know which move that would be.

Secondly, as White, I always develop my King's Knight to f3, not to e2. This is a plus for 3. Nf3, since if I'm going to develop it there anyway I might as well do it right away on the third move.

Thirdly, I like playing (as White) the Exchange Variation (of the Queen's Gambit Declined) very much. Not with Ne2, f3, e4. I play it with Nf3 and a minority attack on the Queenside. This is a plus for 3. Nc3, since it's impossible to get a good position in the Exchange Variation if you begin with 3. Nf3 which loses a tempo.

And lastly, against the Slav, after 1. d4 d5 2. c4 c6, I prefer to play 3. Nf3 over 3. Nc3, because I heard that 3. Nf3 was much more solid and quiet, and that 3. Nc3 can lead to very sharp positions. For example: 3... e5!? looks sharp and crazy, it's possible after 3. Nc3 but not after 3. Nf3. This is maybe a plus for 3. Nf3, since if I already play 3. Nf3 against 2... c6 maybe this means I should also play it against 2... e6.
In the Queen's Gambit Declined, after 1. d4 d5 2. c4 e6, what is the difference between playing 3. Nc3 and 3. Nf3?


With the 3.Nf3 move order your opponent can obtain a favorable position, almost entirely destroying your advantage.

Here is a small example:

[Title "Black dodges the Exchange variation"]
[fen ""]

1.d4 d5 2.c4 e6 3.Nf3 Nf6 4.Nc3 Be7 5.cxd5 ( 5.Bg5 O-O 6.cxd5 Nxd5! ) 5...exd5 6.Bg5 c6 7.Qc2 ( 7.e3 Bf5! ) 7...g6! 8.e4!? ( 8.e3 Bf5! ) 8...dxe4 ( 8...Nxe4? 10.Bxe7! ) 9.Bxf6 Bxf6 10.Qxe4 Kf8!? 11.Bc4 Kg7 12.O-O Re8 13.Qf4 Be6 14.Bxe6 Rxe6 15.Rfe1 Qd6! 16.Qxd6 Rxd6 17.Re8 Rd8 18.Rxd8 Bxd8 19.Re1 Nd7=


With the 3.Nc3 move order, you are on the correct path towards the Exchange variation, but Black has a choice to sharpen the game. He could play 3...c6 offering you the Marshall attack, and even if you decline the offer and try to steer into the Exchange line, he could play ...dxc4 ( immediately or in the next move ) sharpening the game. Do not forget that Black may decide to play ...Bb4 entering the Nimzo-Indian defense which leads to open, dynamic play in most cases.

Be aware that you can not dodge sharp battles with the Nc3 move order, but it is the only correct path to a solid Exchange variation for White.


  Firstly, I am an extremely positional player, I don't like sharp and crazy games full of tactics. I would prefer the move which in average leads to the most solid, positional, slow, closed, strategic and quiet positions. I don't know which move that would be.


You can't achieve what you ask for 100%, since Black has a say too. The best you can achieve is "healthy compromise" -> you can get a positional battle without crazy tactical sparks, but the game will still be dynamic and sharp.


  Secondly, as White, I always develop my King's Knight to f3, not to e2. This is a plus for 3. Nf3, since if I'm going to develop it there anyway I might as well do it right away on the third move.


With the 3.Nc3 move order you can just play Nf3 anytime you want. The point is that you have a choice, that is all...


  Thirdly, I like playing (as White) the Exchange Variation (of the Queen's Gambit Declined) very much. Not with Ne2, f3, e4. I play it with Nf3 and a minority attack on the Queenside. This is a plus for 3. Nc3, since it's impossible to get a good position in the Exchange Variation if you begin with 3. Nf3 which loses a tempo.


Again, the only correct path towards the solid Exchange variation is with 3.Nc3 move order. You can choose between Ne2 and Nf3, it is a matter of taste, but know that Ne2 is a critical line for Black in the Exchange variation.


  And lastly, against the Slav, after 1. d4 d5 2. c4 c6, I prefer to play 3. Nf3 over 3. Nc3, because I heard that 3. Nf3 was much more solid and quiet, and that 3. Nc3 can lead to very sharp positions. For example: 3... e5!? looks sharp and crazy, it's possible after 3. Nc3 but not after 3. Nf3. This is maybe a plus for 3. Nf3, since if I already play 3. Nf3 against 2... c6 maybe this means I should also play it against 2... e6.


Against the Slav move order, you have time before playing 3.Nc3 as he can't respond with a fast ...Bf5 so I would make an exception there and play 3.Nf3 to rule out any sharp play. 

Still, I would go for other quiet lines against the Slav, instead of trying to enter the Exchange variation of the QGD. You should consult opening manual to see if there is a safe transposition, otherwise you might get tricked into an inferior position. This should not be a problem as far as I remember, since there are lots of quiet lines in the Slav for White that suit your style.

SUMMARY:

Against QGD play Nc3 and enter your favorite line, but against the Slav stop early sharp lines with Nf3, and do not attempt to transpose into the Exchange variation of the QGD. Instead, head for the lines with Qc2 or similar, these will suit your style.

If you have further questions leave a comment. Good luck and best regards.