So, who gonna win?

Shogi can use their opponent's captured pieces so it has the advantage.

Shogi since you can bring back pieces on the board.

but you only use pieces facing towards the opponent, right? So what happens to the chess pieces that are brought back (besides the knighted horse)? Do they just stay on the board as neutral parties? Get taken over by a third person who takes a corner of the board and turns it into Switzerland?