user4327: I was recently in a situation in which my bishop was pinned with my queen behind it and my only options were 
- losing the bishop. 
- defending with the rook which would allow an exchange of my rook for his bishop.  
I know both cases are bad but, which one would be worse, or should I say less bad? It could maybe depend on the position as well but I'm looking for an "in general" kind of answer.
Thank you.

user7500: An Exchange (rook for minor piece) is probably worth less than 2 pawns, while a piece averages over 3 pawns. Petrosian once said that the exchange is worth only one pawn.
If you are interested, you could read more about this (and other material imbalances) at this page.
Also, Andrew Soltis' book "Rethinking the chess pieces" is definitely worth a read.

user7297: In general, it is better to be an exchange (rook vs. minor piece) down than a minor piece. If you look at the standard table for piece value, you see that being an exchange down is only 5-3 = 2 points, while being a minor piece down is 3 points.

user825: It's more than just a pawn difference (as stated in other answers). Being an exchange down, you'd still have a minor piece playing against the rook. This is not always a disadvantage, as a knight with a good outpost or a bishop with good diagonals actually value as much as a rook. Your knight could still potentially fork your opponent's queen and king, your bishop could also potentially pin your opponent's queen. Your opponent would still need to prove the exchange advantage to win.
However, being a piece down you would have less chance to come back in the game. Generally, you should not hesitate to give up your exchange to save a piece.

4327: <p>I was recently in a situation in which my bishop was pinned with my queen behind it and my only options were 
- losing the bishop. 
- defending with the rook which would allow an exchange of my rook for his bishop.  </p>

<p>I know both cases are bad but, which one would be worse, or should I say less bad? It could maybe depend on the position as well but I'm looking for an "in general" kind of answer.</p>

<p>Thank you.</p>
 7500: <p>An Exchange (rook for minor piece) is probably worth less than 2 pawns, while a piece averages over 3 pawns. Petrosian once said that the exchange is worth only one pawn.</p>

<p>If you are interested, you could read more about this (and other material imbalances) at <a href="https://www.chess.com/article/view/the-evaluation-of-material-imbalances-by-im-larry-kaufman" rel="nofollow noreferrer">this page</a>.</p>

<p>Also, Andrew Soltis' book "Rethinking the chess pieces" is definitely worth a read.</p>
 7297: <p>In general, it is better to be an exchange (rook vs. minor piece) down than a minor piece. If you look at the <a href="https://chess.stackexchange.com/questions/2409/how-many-points-is-each-chess-piece-worth">standard table for piece value</a>, you see that being an exchange down is only 5-3 = 2 points, while being a minor piece down is 3 points.</p>
 825: <p>It's more than just a pawn difference (as stated in other answers). Being an exchange down, you'd still have a minor piece playing against the rook. This is not always a disadvantage, as a knight with a good outpost or a bishop with good diagonals actually value as much as a rook. Your knight could still potentially fork your opponent's queen and king, your bishop could also potentially pin your opponent's queen. Your opponent would still need to prove the exchange advantage to win.</p>

<p>However, being a piece down you would have less chance to come back in the game. Generally, you should not hesitate to give up your exchange to save a piece.</p>
