Bughouse has to be a nightmare because it's two seperate games which nevertheless have to be linked, and the ability to place pieces makes things crazy. As for Fischer Random (aka Chess960), part of it is relatively easy, in programming the starting positions and randomising, but nailing down how castling works, for example, is rather tricky, especially depending on how the original chess program was coded. I'd still expect it to be easier than bughouse though.
I see that very few chess servers have chess variants. I have friends at the chess club who would very much like to play Bughouse or Fischer random online. I'm not sure if it's really hard to program, but I would really enjoy chess variants on Chess.com.