When you are in a game with 360 and original xbox players, the original xbox players are always given the advantage: their shields regenerate faster, they always win when 2 people melee at the same time, and rocket launchers are more inclined to spawn around them than the 360 players. Also they get overshields and swords on lockout and gemini and sniper rifles on every other map.
So no, to my knowledge there is no advantage in playing on an original xbox vs. a 360.