If I remember correctly, Bust-A-Move was first released in arcades as a dedicated cab, but after a short time it was ported to the Neo Geo MVS (arcade) hardware, which became extremely popular. For that reason, the Neo Geo version is considered the "original" version of the game that all other ports are compared to.
It's been awhile since I played it, but I believe the SNES version is mostly the same, but slightly stipped down. I've never played the 3DO version, so I'm not sure how similar it is.