Look, I'm not talking about strip-mall karate/taekwondo/etc.. I'm talking about arts like Tai chi, xing yi, ba gua, (though I'm not excluding karate/TKD/etc. either) etc. Granted, the lines get extremely blurry, but basically, I'm talking about family systems and monk systems. MMA is just a mish-mashed smorgasboard of oversimplified, crude versions of the real arts. A skilled practitioner of one of the "pure" family systems can easily defeat the biggest, most muscular, fastest, strongest MMA fighters.
My point is, a high-quality family system can defeat a low-quality mishmash of oversimplified arts, which is what MMA is today.
What's a high-quality family system? That's not easy for a newbie to find out. You usually need several years of training in a very average system to even get good enough to judge the skills of other practitioners well.
Also, most of the better systems don't let just anybody study. You usually have to do a few years of the basic stuff before being allowed to learn the real stuff, although there are some rare exceptions.
So, to sum up, if you study with the best in the world in all of the following: Muay Thai, Greco-Roman, boxing, sport TKD, etc., you are still not going to have the skills to defeat a high-level fighter in one of the better family systems.
To be fair, the best fighters in the family systems usually learn at least a little grappling, kicking, boxing, etc. The differences between the best systems are pretty small, once you get to the highest levels.
Meanwhile, though, I'd put myself against any of the MMA fighters in a no-holds-barred match, and maybe even an MMA-style bout, and I'm only about 140 pounds, and 5'8". It's not size/speed/strength, it's training. I am extremely fast, but that's not why I feel sure of my prowess. I was fast before I got the best of my training, but I wasn't nearly as good then.
I'd also put any MMA fighter against thousands of pot-bellied Chinese grandfathers who have taught high-level tai chi, ba gua, etc.. Those old guys, the better ones, could easily beat Ken Shamrock, et al.
If you don't believe it, you can fight me, or I can direct you to some of my fellow students, or I can point you to the parks in the bigger cities that have large Chinese populations, including New York, San Fran, and any city in China. Good karate and TKD systems are also quite badass, although not quite at the same level, I think.