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I understand that this can be very situational which is why I don't provide a position as I am seeking some more generally applicable answer or things to consider.
Assuming that the opponent has a bishop pair would you feel that a combination that leaves me with doubled pawns and the opponent with only one bishop (but no other difference in material). is worth it? I guess another way to ask the same question is whether doubled pawns are a half point disadvantage.
In general, the two bishop advantage is worth half a pawn, while double pawns are only a minor disadvantage. Sometimes doubled pawns can be an advantage if they do not block your pieces and control important squares. OTOH, creating doubled isolated pawns on a half open file is likely to be worth the loss of a two bishop advantage.
Long term imbalances that occur early in a game are easier to deal with than those that occur late in a game. Let us take for instance the Nimzo-Indian line
[FEN ""]
1.d4 Nf6 2.c4 e6 3.Nc3 Bb4 4.a3 Bxc3 5.bxc3 c5 6.e3 O-O 7.Bd3 d5 8.cxd5 exd5
Black has just allowed white to undouble the pawns that he gave up his dark square bishop to double. The key to understanding this is that the doubled pawns are not such a big deal. Black is looking to keep white's dark square bishop permanently bad (because of the pawns on e3 and d4), while getting good squares for his knights. Black's light square bishop will be not so bad (still bad because of the d5-pawn) and will also look for opportunities to trade his light square bishop for white's.
I take it that you feel that you are at a disadvantage because you have a bishop and a knight against a bishop pair in a reasonably open position. (If the position were closed, having the knight might be an ADvantage.)
Most likely, your knight would be pinned by one of the opposing bishops, and this pin would result in a doubled pawn. I can think of two main cases.
1) If the exchange of the opposing bishop for the knight and a doubling of your pawns results in bishops of opposite colors, that would probably be a good result for you, because this situation is the one most likely to result in a draw.
2) The exchange of the opposing bishop of opposite color for the knight (leaving bishops of the same color). That's probably not nearly as good. Then the freedom of your bishop is the key factor. You still have good drawing chances if your pawns on on the OPPOSITE color of the two bishops, giving your bishop, maximum freedom, while presumably "locking" your opponent's pawns on the same color as the two bishops. If your pawns are on the same color as the bishops, blocking your bishop while providing fodder for his, you have losing chances.
The bishop pair is usually stronger than B+N or N+N. While doubled pawns are usually weaker than two adjacent pawns. My advice is to look at the pawn structure and king placement to guide your decision whether to allow your opponent to exchange a bishop for your knight and leave you with a doubled pawn. Let's start with the Spanish system
[FEN ""]
1.e4 e5 2.Nf3 Nc6 3.Bb5 a6 4.Bxc6 dxc6
practice has shown that black can handle this type of pawn structure by following the correct strategies. Next, in the Trompowsky attack
[FEN ""]
1.d4 Nf6 2.Bg5 h6 3.Bxf6 exf6
the light squares (d5, e4, f5, f7 and h5) become sensitive for black and white is better.
Next, the following silly example
[FEN ""]
1.d4 Nh6 2.Bxh6 gxh6
shows that black simply cannot accept this sort of pawn structure to get the so called "bishop pair advantage". I would recommend to study and think about the bishop pair versus B+N or N+N situations. As well as delve a bit deeper into pawn structures and weak squares. Here are a few possible guidelines
To directly answer the OP as asked looking for a general answer.
NO.
And it is unlikely you will get to choose.
In many cases if they wish to give up the bishop pair you may have to take the doubled pawns and have nothing to say about it.
