To capture or not to capture on f3 - that is the question

Another question regarding the opening: When to capture a Knight with a Bishop on f3/f6 (c3/c6) and when not to, after a6/h6 (a3/h3)? This is another question I would appreciate some thoughts on. Most often it seems as if it is better not to capture with the Bishop, exchanging a Bishop for a Knight. But in some positions, Chessbase and/or my engines highly recommend capturing. But it is not at all obvious to me why it is sometimes better to capture. 

Here is an example: 

To capture or not to capture? That is the question.  

I hope someone can cast some light on this. Thanks.  

I would be tempted to capture due to the fact that your pawns are already on light squares and can compensate for the lack of your light squared bishop. Retreating the bishop loses time, and the fact that the centre for the mean time is closed means the bishops will not be an immediate advantage especially because white has blocked their c pawn temporarily. Seeking play on the dark squares where you're stronger would be a good idea but I'm not sure how your go about it, maybe advance on the queenside and try to weaken b4/c3/a3 somehow.

Thanks. However, I am asking since both Stockfish and Komodo says ...Bxf3. Most often the engines recommend not taking the Knight. Here they recommend capturing. Why is what I don't understand. Any thoughts? 

 Also if white wants to open the position for their bishops they will need to be willing to accept an IQP (not sure if this is a disadvantage as it will give them plenty of activity) or prepare c4 with b3 and weaken dark squares and be prepared for hanging pawns. I don't know enough about pawn structures to assess those positions but I think it's important to note.

Usually, I'll maintain the pin as long as possible.

In this case, though, maintaining the pin will put black in an uncomfortable position, after:

Now white is threatening h4-h5, trapping the bishop. Trying to save the bishop will run into other positional problems for black.

This is why, in this position, Bxf3 makes more sense. The bishop pin on the c6 knight is what makes white's tactics possible in this line. Which is why, as black, I would've played ...a6 before this point, to eliminate the pin on the c6 knight.

(Rule of thumb: Don't leave your pieces pinned, if you can help it.) 

 It really depends on the situation.  In this case black would be trading its bad bishop for a knight that will likely end up being very annoying once it gets to e5.  I probably lose the bishop pair after g4 and Ne5 (if white wants). Plus the pawn structure is likely to stay closed. 

If I am white and a6 is played I don't trade.  Trading moves blacks b-pawn to the c-file  where he can undermine my d-pawn, probably opening up the pawn structure and making the bishop pair more valuable.  I don't see any upside as that bishop is great on d3

Thanks a bunch, guys. This gave a lot of food for thought.  

Not exchanging means maintaining the pin, and keeping white under pressure. However, in this particular setup, it seems that g2-g4 is perfectly playable, followed by Ne5- so taking the knight does look like the indicated solution.

This is how many of my games continue in similar positions.  Black gives up material in return for exposing White's king and maintaining the pin.  It works well against me, but that may be because I'm a run-of-the-mill player 

How do you intend to "maintain the pin" after the simple 11.Qd3? There is no pin there, already!

IM pfren

I was speaking in general rather than specifically to the given position.  Usually when I am playing Black, my opponent will make the knight for two pawn exchange, and I am left with an exposed king and and a pinned knight.  Usually my opponent will have a bishop on b3 aimed at f7.  Typically, my opponent has castled, and in exchange for the exposed king, I have a super highway for a rook down the king side.  At my level, it gets pretty complex.