NHL has this one.  Then it's a battle between NBA and MLB.
Now, to make this more interesting, any piece of athletic equipment can be used.  If that was the case, this is how it would play out:
Everyone would fuck up the basketball players first, then it would be a battle between NHL, MLB, and NFL.  As much as the helmet helps, the bats, baseballs, sticks, and pucks fuck them up bad.  Now here is the real battle- Baseball vs. Hockey.  This is a tough one to determine, but it could be baseball.  First, the pitchers stun hockey players with 90+ mph pitches, then go club the fuck out of them with the heavy wooden bats- that's a lot of mass coming at your head, one hit and you're fucked up.  So if gear could be used, baseball would probably win, unless the NHL players took the blades off their skates and made ninja stars and boomerangs to fuck up the baseball players.
No matter which fight scenario it is, as long as the Red Sox and Yankees get fucked up the worst, everything is okay.