NBA - some of these guy might have the instincts or experience, but the NFL would break em like twigs. Besides, most are probably out of experience with their gangsta self, so they're out.
MLB - With enormous clubbers like Bonds, MacGuire, and the like swings baseball bats and even old timers like Clemens likely to take someone's head off with a fastball they should do well. Except, these are the guys that are armed when they get hit in the head, and forget to bring the bat when charging the mound. They're brawling experience involves throwing chairs into the stands, and playing matador with 80 year old managers. No good for a brawl.
PGA - Sorry, thought this was a sports brawl. If they dared even show up in the stereotypical golfer outfits, every other sports group would unite to beat the living snot out of them, and their caddies for good measure.
Tennis - Not much muscle for these guys, and no matter how hard they can hit a tennis ball, the NFL players could just shove some lineman up front as human shields and charge them for a mauling.
Soccer - Ok, they actually stand a chance. Not because they're that tough, but because there's about nil opportunity to keep their fanatical fans out of this. It would come down to how many soccer fans would be available to swarm the other sports teams. If they get anywhere close to 10:1 odds, the mob might pull it. And hey, those soccer players are good at feigning injury, so in a brawl they might be able to sneak in a good shot, and get away, or play dead to survive.
Jockeys - You gotta let the midgets take their shot, just because a brawl with midgets is is just a better brawl. Without their horses they're dead in the matter. With horses, they might be able to trample and flank enough to last long, but eventually they'd become the top target for all survivors and get swarmed.
NFL - You gotta love the biggest baddest boys out their. They've got size and speed on almost everyone, and are probably the most physically gifted faction. They're likely to be the chic pick, but underdogs to actually win.
NHL - Half of playing hockey is knowing how to brawl. Scott Stevens could take down most entire factions in this brawl himself I would think. Get some more players like him who seem to look up to the Broad Street Bullies as role models, and you're well on your way to winning. This is a league where goalie fighting is optional, but encouraged when the team goes into a brawl, however only optional because of how long it takes for them to get enough padding off to fight effectively. These guys are a mix of experience, underhandedness, and physical toughness (can anything other than a "war of attrition" adequately describe their playoff system?") that would be hard to topple.