Bishop or Knight?

Is a bishop or a knight better to use later in the game?
Because I will almost always sacrifice my knight for the opponents bishop.

This game opens 1. c4 c5 2. Nc3 Nc6 3. g3g6 4. Bg2 Bg7 5. e3 e5 6. Nge2 Nge7 7. b3d6 8. Bb2 0–0 9. 0–0 Rb8 10. Nd5 Nxd5 11. cxd5 Nb4 12. d3 b6 13. a3 Na6 14. Qd2Nc7 15. d4 exd4.

In this notebook, Fischer comments that Petrosian employs an “interesting system for Black.” Indeed, after the more or less forced sequence 16. exd4 Ba6 17. Rfe1 Bxe2 18. Rxe2Nb5 19. dxc5 Bxb2 20. Qxb2 bxc5, Petrosian, playing as Black, had a clear positional advantage due to the superiority of his knight over White’s bishop.

Fischer (as Black) had defeated Petrosian in the 1970 U.S.S.R. vs. the World match with the variation starting with 5. …e6. Fischer was fond of meeting 1. c4 with 1…c5 at this stage of his career, and he may have been looking for a line that stayed close to home and sidestepped any improvements Petrosian planned after 5. …e6. The chance to play one of Petrosian’s weapons against him would have supplied an extra psychological benefit. This line did not appear in the match as Petrosian opened 1. d4 in game 2, 1. Nf3 and 2. b3 in game 5 and again 1. d4 in game 6. The closest it came to occurring was game 4 which opened 1. c4 c5, but Petrosian varied with 2. Nf3.

http://worldchesshof.org/exhibitions/exhibit/a-memorable-life-bobby-fischer/

Which should be better?

It depends on the position.

Knights need a base of operations because they're short range pieces. That is to say, a protected square.

Bishops are long range and can operate from a distance.

Neither like to be blocked by pawns. So in the endgame, where there are fewer pieces to block movement, the speedy bishop is generally happier. But sometimes even in the endgame there are many friendly pawns on its color so it's not very mobile. Also, sometimes a knight will have a support point that puts it in the heart of the position, attacking all the squares around it like an octopus. In such cases the knight can be extremely strong (worth more than a rook).

So in each position, look around the board and you'll usually find you have 1 or 2 good minor pieces (minor pieces are the bishops and knights). They're good because they're not blocked by their friendly units, they are attacking the enemy, and in general they're centralized.

You'll also often have 1 or 2 mediocre or bad pieces (blocked by friendly units, especially pawns, or on the edge of the board away from the action).

The trick all strong players use is to try not to be left with the bad pieces! So before trading your good ones, try to improve your bad ones. There's some old saying that goes something like "beginners play with their best pieces, masters play with their worst."

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This is likely the best advice I've ever given on a bishop vs knight topic lol  (And I've seen them here for years.)

Bishops are long range pieces

Knights are short range pieces.

Since bishops are long range they thrive in open positions.

Since knights are short ranged they thrive in closed positions.

In the opening phase of the game.

The board is considered Open.

Bishops are slightly favored over Knights because they are long range.

Knights can't control as many squares in there starting position.

Which is why some chess coaches tell students to develop knights before bishops.

The idea is to develop your worse piece first.

Since knights are short range it is considered good to develop them first to improve them.

In the middle phase of the game.

The piece which is better is determined by the landscape (I.E The pawn structure)

If the position is open with few pawns remaining.

Than the bishops would be favored.

If the position is clustered with a bunch of pawns.

Than the knights would be favored.

In the end game

Bishops are often favored in situations were there are pawns on both sides of the board.

Since the bishop is long range they can attack both sides really fast.

The knight would struggle in trying to attack both sides since it is short range piece.

If the pawns are on only 1 side of the board or if there is a cluster of pawns than the knight can be better than the bishop.

One very good metaphor I will give you is based on Medieval times!

Think of bishops as archers.

Think of knights as swordmen.

As long as the enemy stays far away the bishops (archers) will always be the favorite.

Simply because they can keep shooting stuff down.

If the battle is close ranged than the knight (swordmen) will be favored.

Bishop for open positions*.

Knight for closed positions.

*If the pawns control light squares and the bishop dark squares or vice versa, then the bishop is 'good.' Otherwise, if the bishop's sight is covered by friendly pawns, then it's 'bad.'

>sacrifice my knight for the opponents bishop

That's not how it works.

>sacrifice my knight for the opponents bishop

That's not how it works.

That's what she said 

You don't "sacrifice" a knight for bishop, especially without context.

Of course you do!

Fischer called it "Minor Exchange" ahead 

It's not a sacrifice, they're worth the same.

The bishop pair gets a small bonus... but this only matters if you're good enough to use it. And of course it can be negated by other factors.

Honestly, other than: "active pieces are better than inactive pieces," all of these bishop vs knight considerations are irrelevant to your results.

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The minor exchange refers to the capture of the opponent's bishop for the player's knight (or, more recently, the stronger minor piece for the weaker. 

Traditional chess theory espoused by masters such as Wilhelm Steinitz and Siegbert Tarrasch puts more value on the bishop than the knight. In contrast, the hypermodern school favored the knight over the bishop. Modern theory is that it depends on the position, but that there are more positions where the bishop is better than where the knight is better.

Later on in an open position the bishop is very powerful. In an open position it can attack and defend both wings. That is why the bishop in the endgame gets around rook 's value. But it depends again. If the bishop is in the center and all opponet pawns are the opposite color of the bishop and black has a knight position is somewhat better for black.