Depends what era. Pretty sure Kirk would get into a badly acted out wrestling scene with one of them, but Picard would lay down his weapons and cross his fingers (if he knew there was next to no chance he was ever going to get off the planet). Klingons would survive the longest if you don't count that Predators wouldn't attack Starfleet if they dropped their weapons. Klingons are used to fighting, and they have hard exoskeletons. Cardassians and Vulcans (Romulans too, obviously) possess superior strength [to Humans] too but are not warrior races. At least, not as much as Klingons. The Romulans are pretty Xenophobic and might even start going a bit mad and paranoid. They'd probably go down first. Then Cardassians, then the Klingons. It also depends on what weapons they have. Hand to hand combat, do they each have their races combat weapons (Vulcan Lirpas, Klingon Bat'Leths etc) or are they carrying Beam weapons?
I think the Humans would be the only one willing to put down their weapons, once it was discovered that the 'Predators' only hunt armed prey. The other races are too proud, agressive or paranoid to risk laying down arms at the chance they wouldn't be hunted. ;) It's also likely they would all survive, since Star Trek technology seems vastly superior to that of the Predators.
I would have to say the klingons, think about it they're natural born survivors, plus there physical strength pretty much would allow them to over-power the Romulans, and the humans, but the Cardassains would probably pose the most challange. Nevertheless when ever you watch any episode the humans have there ship above them to help them one away or another, without there precious starship the humans would be gone for good in the first 20 minutes.