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@AThousandYoung saidPut the king in the corner and it has 3 moves, knight as 4. Knight can jump over pieces, can move in different directions and can attack numerous pieces at once.
Ignoring checks etc...
Both control 8 squares. King is precise but slow. Knight can cross map faster but suffers more near the edge of the board.
Are both equally powerful?
It's not even a debate.
3 edits
@A-Unique-Nickname saidA knight in the corner does not have four moves, it has two.
Put the king in the corner and it has 3 moves, knight as 4. Knight can jump over pieces, can move in different directions and can attack numerous pieces at once.
It's not even a debate.
The relative value of the two pieces depends on the position. For example, a White K on e7 w/ a P on d6 can force the P to promote against a lone Black K, because the White K controls d7 and d8; a lone N supporting the P cannot, if the opposing K is near.
On the other hand, a White N can give smothered mate to a Black K in the corner, whereas a White K cannot.
@AThousandYoung saidAre both equally powerful?
Ignoring checks etc...
Both control 8 squares. King is precise but slow. Knight can cross map faster but suffers more near the edge of the board.
Are both equally powerful?
Generally, Knights are better in closed or congested positions, while bishops are best when there are fewer pieces on the board. There are a number of exceptions to this however depending on a given position.
https://en.wikipedia.org/wiki/Chess_piece_relative_value
During the endgame, as there is less danger of checkmate, the king will often assume a more active role. It is better at defending nearby pieces and pawns than the knight is and better at attacking them than the bishop is.[10] Overall, this makes the king more powerful than a minor piece but less powerful than a rook, so its fighting value is about four points.
1 edit
As has been mentioned, a lot depends on the position. There are good and bad points in favour of
each piece. If you take a very common endgame tactic, attacking an unprotected blocked pawn.
In the left hand position the King can do it one move from three different squares capturing the
b5 pawn on its second move. It takes the Knight three moves to attack it, capturing it on its fourth move.
In the right hand position. it is nearly the complete reverse. It takes the King four moves to capture the g5 pawn,
the Knight two moves. The slight difference being the Knight can only do it from two squares. (f3 and h3)