I assume it works just like Diplomacy. Meaning they both bounce. Unless one of them has support to move by another piece, and that piece itself is not under attack.
Both dead!
Or a d20 roll to see who survives based on how many times you have upgraded your units!
Maybe in chess3 :D
I tried it, queen and bishop to the same square, they captured each other and disappeared off the board!
I don't think that is possible given the potential moves and the board.
> I don't think that is possible
I think you mean "likely" rather than "possible". It's definitely possible. I had it happen.