There come certain points in games of chess where your opponent would seek to exchange a piece with one of yours, usually with the idea of gaining a strategic position on the chessboard. In most games that I've played, piece trade-offs would involve the knights and bishops, considered second only to the rooks and third to the queen, at least, in my opinion. The question is this: which is more important in said exchanges, the knight or the bishop?
Let"s start by evaluating individually each chess piece:
The knight's movement across the board is an 'L' shape. As such, it can be quite versatile in the game in comparison to a bishop, considering a bishop can only move diagonally across cells of the same colour, whereas a knight can alternate between the light- and dark-coloured cells as it moves.
However, it requires much care on your part to place your knight early in the game on the opposing side where it would actually be in a position to check your opponent's king, partly because of the still intact line of pawns preventing the knight from coming anywhere near it. The second shortcoming of a knight is its ability to cover a limited range of cells on the board, as opposed to the bishop, rook or queen.
Screen shot by me from chess.com.
Shown here is the endgame of one of my most recent games, where the white king is threatening a passed pawn on my side by removing the only obstacle in sight, the last black pawn. By placing my knight on d5 in two moves, I was just able to prevent the white pawn from advancing any further than b6. It was only after moving my king to its knight and chasing the black king around the knight, that my opponent finally decided to draw the game with me.
As mentioned above, the bishop moves diagonally across cells of light- or dark-coloured cells, depending on where it's placed at the start of the game. Unlike the knight, it could easily become a threat to your opponent's king early in the game by targeting the weakest cell, that is, the one protected by the king itself.
Bishops, however, are the only pieces incapable of being linked with each other, as they move only in squares of different colours, unlike the rooks or knights. The queen is the only piece able to link with either bishops in diagonally breaking through your opponent's defence, considering it can also move diagonally across cells of either colour.
It all comes down to determining how well placed your pieces are before making the exchange with your opponent. Doing away one of your bishops would give your opponent a strategic advantage on the squares of the concerned colour, whereas the removal of one knight in your arsenal would mean less flexibility in your gameplay. Either way, handle all your piece exchanges with extreme caution, preferably in the direction of your opponent's eventual checkmate.