No home port prior to consoles being able to emulate the arcade game can compare to the arcade game. The Sega CD release does add a time attack mode that is interesting and can be challenging. The other home ports do not add anything, they each have taken away, unfortunately.
None of the arcades around me back in the day did anything like yours did. That is awesome that they did that.
RE: Final Fight Brings Arcade Home on Super Nintendo - September 1st, 1991 - Today in Video Game History