Basically, Sam Stone nailed it.
Early UFC MMA fights had some really rough lop-sided fights. A few karate, tae-kwon-do, kenpo guys did ok, but alot of them got pounded buy a guy that just overwhelmed them with punches to the face.
The best way to win an MMA fight these days, is to land so many punches in a row, that the ref calls the fight (usually the guy is ko’d after a good salvo of punches).
One can get a submission via a choke, which is easy if the opponent does not guard themselves well. Consequently, any fighter in a chokable position is highly aware that they are in danger of said choke. Same goes for joint locks (arm bars, ankle locks, kimuras, omaplatas (sp?)). They are effective, but good fighters know when they are vulnerable to them.
I was a purple belt in Kempo (yes with an m) and decided that I didn’t want to have to beat the shit out of someone to survive. Punching and kicking is only usefull if you can deliver heavy blows.
I tried Aikido, and loved it. My Sensei had MS, couldn’t walk without crutches, and could kick anyone’s ass you could think of. There were limitations though. Aikido is a very effective martial art if one is engaged in a stand up fight. It is all defensive, and ultimately immobilizes you opponent via joint locks, center of gravity manipulation, and momentum reversal. It is not usefull if you have a guy sitting on your chest that is punching the shit out of you though.
After weeding out the impractical martial arts, the only real elements that remain effective are those of boxing, muy thai, Brazilian ju-jitsu, and Greco-roman wrestling. The vast majority of MMA fighters win using an element of one of the aforementioned styles these days.
If Jackie Chan (or even Bruce Lee for that matter) fought like they do in movies (meaning various annoying strikes that do little real damage) they would get the shit kicked out of them. A more muscular fighter would absorb a few blows, take them to the ground, and either submit them or pound them untill stoppage.
As Cerowyn said, Pride is a bit more respected internationally as opposed to UFC. They do have one of the best MMA fighters in the world too Fedor Emelianenko. He hurts people.