I think in this instance, Laz and Mega are both correct. Today most fighters in the UFC have adapted the same style and have learned how to defend against moves Royce Gracie did. I think if you had a much bigger opponent(20lbs+) he would most likely win do to sheer size and leverage as Laz mentioned.
However, before UFC became well know and more organized it was more of a brawlers game. Royce Gracie did then, what is done now. Back then, most had no idea how to stop it and so he was very successful. Here's a site with some info of his fights...
http://www.fightingmaster.com/legends/royce/ Here's a little snip:
Six months later Gracie is back at UFC 3 defending his title as the Ultimate Fighting Champion. His first match was against Kimo Leopoldo, a tattooed giant that outweighed Gracie by 80 lbs. Gracie won with an armlock, but had to be helped out of the ring as he was completely exhausted, and did not return to action that night. Three months later he returned to action in UFC 4, tapping Dan "The Beast" Severn in the finals.
The only guy I recall hanging with him is Ken Shamrock who fought him to a draw. And the only guys that I've read that have beat him are guys his own size that fight with his same style. I don't think he'd do so well today b/c everyone has adapted his type fighting style and he even trains some of them now.
