the bishop would have a significantly easier time as the bishop has more mobility. although there can be a case made for the royal knight as they have bishop pair and the knight is also quite difficult to capture, however I think with the kings on the board the game will be a lot more closed and unlikely to cause any significant damage
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For white, the knight is a royal piece, and for black, the bishop is a royal piece. However, both castling is possible, and the Pawn can be promoted to King, Queen, Rook, Bishop(But it not a royal piece), or Knight(Not royal either). The game does not end even if the king is captured.