I have a ton of Judo experience, some MT, and a little bit of Greco, and a fair amount of MMA, and I'd say that the Thai clinch is the closest to MMA only because it's the only one where you have to deal with strikes and potential throws (though obviously a reduced arsenal, and you don't have to worry about your legs at all). The Thai clinch is all about breaking posture and opening up angles to throw knees and elbows, the throws are mostly incidental if you can catch someone off balance or as a counter to a knee. NM do get their hips in very close and worry about keeping inside position and getting underhooks or very strong overhooks because those things are useful for doing damage without taking any, but they worry very little about locking their hands, though there are body lock throws in MT and they're fairly common if guys are slow to drop their hips down when they get out-clinched. Keep in mind too that a low clinch like you'd have in folk is not common in MMA as it will get you kneed, the clinch resembles Greco/MT much more than it does any sort of collar + elbow like you might see in collegiate or freestyle wrestling.
I'd say from a clinching standpoint (that is to say, ignoring the total lack of sprawl or other shot defense) the biggest deficiencies for your average MT guy are going to be a susceptibility to reaping throws and bodylocks of all sorts. You can't reap in MT, and while you can body lock as I mentioned the fact that you're wearing the big gloves makes it hard for the thrower to get a really strong grip, so you can usually stall out to a ref break just by squatting slightly and dropping your weight. I would expect a guy like Buakaw's balance and basic position and handfighting to be pretty good, but he definitely wouldn't be used to some really common MMA clinch techniques like outside trips.
