I agree. Taking with the Queen is the better option.
Pawn structure

I don't think it's as simple as one capture is better than the other. It's just two different ways to play.
Taking with the queen "preserves your pawn structure". Whatever that means. I guess there is some fear of doubled pawns. If you take with the queen you can challenge black's d5 pawn with c4, which is good.
But, taking with the pawn also has its plusses. White now has an extra central pawn, and this allows him to fight for the center by playing e4. White also has the half open c-file which might be very useful.

Exactly.
The one with 3...e6 4.Bxf5 exf5 isn't quite as good, I think. It's a doubled pawn, and one fewer pawns in the center. But still, a half-open e-file in return, and full control over the e4-square (if black wants to challenge it with f2-f3, his pawn on e3 will be weak). At some point black may contemplate breaking with f5-f4.
But overall I'd prefer white there. I'm sure there are stronger players than me who'd like to play it with black, though.
Generally speaking, after ...Bxd3, Qxd3 is usually the right move - I think you have to see something quite specific to want to capture with the c pawn.
The Bxf5 exf5 conundrum is a rather more difficult one though. This one is *extremely* position-specific - sometimes it's ok/good for Black, sometimes it guarantees an edge for White. Weighing it up is not at all easy.

I'd look at it another way (and probably not move Bd3 at all). Why answer Bf5 with Bd3? Is that exchange good for me? I've already played d4 and e3, so I've got my pawns lined up on black squares. I probably want to keep my white bishop, not trade it! What I'd really like to do is win a tempo attacking that loose bishop of his on f5, or also good, exchange it for a N making my White bishop really strong. His Bishop on f5 doesn't accomplish much but it does tie my Q to the defense of the c2 pawn. Why not move that c-pawn, freeing my Queen for duty, and allowing a host of other good things I'm too lazy to list here.
So after Bf5 I think c4 is my move rather than Bd3.
However, that analysis helps answer the original question. Suppose we did move Bd3 which was answered with Bxd3. How to retake? Qxd3 seems like it leaves the Q on a perfectly ok square, and it leaves the pawns unmolested, so it seems a perfectly natural choice, but I think it's a strategic mistake. After the exchange you no longer have a light squared bishop. Those pawns and your remaining bishop are no longer a good fit, indeed you are well on your way to having a bad bishop. Retaking with the Queen is saying, I like my pawns. You shouldn't. You'd like to move those pawns. I much prefer retaking with the c pawn, this supports an eventual e3-e4, a central space grab that frees your dark square bishop too. e3-e4 is something you are probably going to want to play (although of course the weak d pawn will then be a concern)... with the c2 recapture I dunno, I kind of like the way things are going -- White threatening to eat up lots of center with mobile central pawns. The more I look at it, actually: I don't like Black's Bf5. I think it gives White his choice of (good) plans: A traditional c4, or a c2xd3 recapture that leaves him strong in the center.
I wonder what master analysis has made of this position, I'm sure it's been looked at a million times before.
*Edit* Well, after consulting the game explorer database. Only one game follows my c2xd3 advice and for a while it goes quite well for White, until he blunders badly. Prior to that, c4 is played more often that Bd3 and it does okay. Bf5 is not, at least statistically according to the game explorer, a bad move. I stand by my analysis
JG - he was asking more about the general structure, rather than those specific moves, which were just illustrative.
The problem with cxd3 and a subsequent e4 is that if Black ignores it, exd5 is dodgy for White leaving him with two isolated central pawns, and if White pushes with e5 then it's just a French structure with a pawn worse off on d3 than it would be on c2 or c3.

JG - he was asking more about the general structure, rather than those specific moves, which were just illustrative.
The problem with cxd3 and a subsequent e4 is that if Black ignores it, exd5 is dodgy for White leaving him with two isolated central pawns, and if White pushes with e5 then it's just a French structure with a pawn worse off on d3 than it would be on c2 or c3.
Much of my post is about pawn structure (the part where I "return to the original question" -- the bit about c4 is treating the moves as an opening). I believe the determiner in the 'pawn structure' is which recapture leaves us with better piece activity... cxd3, or Qxd3? Because of the dark square d4, e3, pawns there actually is a clear answer: cxd3. Other people seem to focus on the doubled pawns as a potential weakness. Sure they can become an endgame liability -- but IMO piece activity is more important, especially in the early stages of the game. The stats for Qxd3 (if this is treated as an opening) are quite poor, and are inferior, to the cxd3 stats, btw.
The problem with cxd3 and a subsequent e4 is that if Black ignores it, exd5 is dodgy for White leaving him with two isolated central pawns, and if White pushes with e5 then it's just a French structure with a pawn worse off on d3 than it would be on c2 or c3.
The e5 structure with a 'pawn worse off' than in the french isn't clear to me... a half open c-file to work with is a very useful thing. But at any rate, this criticism might apply against playing Bd3 in the first place, but it doesn't indicate that Qxd3 is the preferred recapture.
Further, I didn't say you can push to e4 willy-nilly. You need to push it when it makes sense, it doesn't need to be played right away. There's only one game in the Game Explorer with this line -- take a look. White does play e4 as I suggested Black does indeed ignore it as you suggested, White eventually plays e5 (exd5 was not good, as you've said) and White has an ok game -- until he blunders:
http://www.chess.com/games/view.html?id=4487623
By move 16 White has a nice space advantage and IMO has chances on the kingside -- but, alas, he obviously isn't comfortable with this position, he fails to generate any play on the kingside -- his h pawn advance is feeble -- and then he implodes with 26.Nb3? throwing his chances out the window.

I think that I would take with the pawn, as now I would have three pawns in the middle, and if you move on foreward, then you have a very strong pawns structure that may not be cracked very easily.

I'd rather have the c4 lever available after Qxd3 then the e4 lever available after cxd3.
You don't like e4. I understand. I think you are discounting the dynamic value of the half-open c-file and of the e4 lever. I'm probably discounting the weakness of that whole central pawn structure after cxd3 -- it's pretty ricketty. In the end I think It's all about that dark square bishop. If the dark square bishop has problems because of e3 consider cxd3... if the dark square bishop is off the board or outside the chain or otherwise gainfully employed, Qxd3 is the first choice.
(Full disclosure: I should probably mention I'm just nuts about that half-open c-file in general. So I'm probably unnaturally drawn to it here. )
White can still play perfectly easy for e4 without the pawn being on d3 anyway. Just ask all those Colle-type systems. No darksquared bishop problem :)

I'm just going to talk about the pawn structure, not if it's accurate to play Bd3. Now obviously you should not be afraid of capturing cxd3 just because it doubles the pawns, but I don't think that is the correct move. First off, the central structure is more exposed than usual (not weak exactly, but weaker). Yes, the d3 pawn supports e4 , but this pawn isn't really needed to support e4,(it's quite easy to play this move without, actually) and it's less flexible, because now e5 might not be a good choice if it means weakening both e4 and e3. The c file is open, but this won't lead to immediate benefit, and besides white could have just played c4 if the pawn wasn't doubled, which would attack d5, keep the pawn structure straight, and if you really wanted the c file opened, then you could play cxd5 at some point. Also, the queen gets developed by recapturing, a nice bonus.
So there is no point in committing to cxd3 when the c file can be opened at any moment with c4, and when moves like e4-e5 won't damage the pawn formation as much. Obviously with the c pawn recapture black is not going to play ...dxe4 on reply to e4, which would justify c takes, but just blockade them. Queen takes looks more flexible to me and quicker developing. It gets in e4 very easily if that's what white wants.
If white indeed plays e4-e5 Jg27Pyth, indeed this isn't a good french type position for him. The c file has nothing to do with white's space advantage, so it's hardly going to lead to anything, it's just a random file. Meanwhile, the base of the pawn chain can't be bolstered by c3, so it will fall much more easily from a ...c5 move, and then e5 will be rather weak.

Elubas, not sure that the d3, d4, e4 pawn structure is that susceptible to a ... c5 push. Since white could take dxc5 and then play d4.

I'm just going to talk about the pawn structure, not if it's accurate to play Bd3. Now obviously you should not be afraid of capturing cxd3 just because it doubles the pawns, but I don't think that is the correct move. First off, the central structure is more exposed than usual (not weak exactly, but weaker). Yes, the d3 pawn supports e4 , but this pawn isn't really needed to support e4,(it's quite easy to play this move without, actually) and it's less flexible, because now e5 might not be a good choice if it means weakening both e4 and e3. The c file is open, but this won't lead to immediate benefit, and besides white could have just played c4 if the pawn wasn't doubled, which would attack d5, keep the pawn structure straight, and if you really wanted the c file opened, then you could play cxd5 at some point. Also, the queen gets developed by recapturing, a nice bonus.
So there is no point in committing to cxd3 when the c file can be opened at any moment with c4, and when moves like e4-e5 won't damage the pawn formation as much. Obviously with the c pawn recapture black is not going to play ...dxe4 on reply to e4, which would justify c takes, but just blockade them. Queen takes looks more flexible to me and quicker developing. It gets in e4 very easily if that's what white wants.
If white indeed plays e4-e5 Jg27Pyth, indeed this isn't a good french type position for him. The c file has nothing to do with white's space advantage, so it's hardly going to lead to anything, it's just a random file. Meanwhile, the base of the pawn chain can't be bolstered by c3, so it will fall much more easily from a ...c5 move, and then e5 will be rather weak.
I think we've established that there's enough to think about that the question is best answered when looking at specific positons...
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Elubas, not sure that the d3, d4, e4 pawn structure is that susceptible to a ... c5 push. Since white could take dxc5 and then play d4.
Loomis - however, the d4 pawn IS susceptible to pressure from Black's pieces (Nc6,Nf5,Qb6) and White can't buffer it with c3.
JG - your post seems irrelevant as an answer to Elubas'. He knows what you mean, those diagrams don't illuminate your point. Read the post again and presume he's talking about your first position.

1...d4 Is your better option. It unleashes a protected pawn controling a couple center squares and if he responds 2....d5 Do:
2...c4. If he captures, move 3...e4 to control the center.
There are plenty of openings to do to control the center, You can even try to make your own. Try this one on your next game(s).
The only lesson one can safely take away from this is to be highly skeptical of advise from fish on the forums.

1...d4 Is your better option. It unleashes a protected pawn controling a couple center squares and if he responds 2....d5 Do:
2...c4. If he captures, move 3...e4 to control the center.
There are plenty of openings to do to control the center, You can even try to make your own. Try this one on your next game(s).
Ok, this is rather naive. That's the IDEAL of 3 e4, but then why isn't it most popular? 3 e4 is fine and it fights for the initiative, but the problem is that black can instead play more actively and attack the pawns at the same time white's trying to regain the pawn. Usually, white regains the pawn, but his central structure is a little compromised (he had to play d5 or e5 prematurely).
Jg, you still haven't told me how all of the benefits of c takes can't be done with queen takes (e4 can be achieved and c4 can open the file, as well as attack the d5 pawn.
Hello,
this is more a question about pawn structure then about a specific opening. After, for example, 1.d4 d5 2.e3 Bf5 3.Bd3:
- if Black takes on d3, should White take with the Queen to preserve his pawn structure or is taking with the c-pawn better ?
- can Black play 3...e6 ? What about the pawn structure after 4.Bxf5 exf5 ?
Thank you very much,
Jerome