In general, a chess set has the king as the tallest piece, followed by queen, bishop, knight, rook and pawn in that order. Notice in the starting position how the piece height decreases smoothly from the centre to the edge. (Also, when buying a chess set, usually the height of the king is given as a guide to the size of the chessmen.)
Thus I would say the king is the taller of the two pieces, which from your picture looks to be the one with the spike on the left.
This ordering of height may not hold for particularly ornate decorative sets.
However, if you're not going to use the set to play against other people in tournaments (where usually Staunton pieces are mandated anyway), the correct answer would probably be: the king is whichever piece you think it is.