ok, before we get a little too far into chop socky land, let's return to reality for a second...
Bruce Lee was a good actor, and an even better martial theorist. He laid the foundation for the whole concept of mixed martial arts that dominate the martial arts world today. Before Bruce, there weren't very many people willing or able to mix and match techniques. His theories and concepts are widely seen as groundbreaking and have really elevated martial arts beyond its rather stiff roots into the modern combat principles that can really be effective for a lot of people.
That said, Bruce wasn't a great fighter. He may have eventually become a great fighter, but he wasn't. He lost or fought draws his most significant opponents in actual fights. One of those fights went on for 15 minutes and Bruce was EXHAUSTED. His opponent wasn't even a master - it was a senior student. Bruce had done so badly in that fight that he scrapped his made up style altogether (Jun Fan kickboxing) and started all over again, laying the foundation for Jeet Kune Do.
Another fight was against Gene Lebell, who pretty much grabbed him in the beginning and put him in a submission lock. Mas Oyama challenged him to a fight and Bruce declined. His reason? He was "mid-style" at the time and was still trying to develop his martial art, so he would have lost. Bruce promised he'd get back to Mas when he was done.
Never happened.
Bruce trained with really great martial artists to incorporate techniques into JKD, but he never actually got around to finishing the martial art. That's why if you look at the three master students of JKD - Taki Kimura, Dan Inosanto and Ted Wong - their JKD has nothing in common with each other. At all. Bruce was notorious for declaring his JKD "crap", closing his school, moving and starting again, leaving his students to wonder, "Did we just learn something bad?".
That's why, despite the fact that JKD is the "root" of mixed martial arts as we know it, nobody really takes JKD that seriously. It's a damn mess. It's not entirely Bruce's fault (he died before finalizing a style that he scrapped almost every year), but that's the way it is.
Maybe if Bruce Lee had studied a real style for more than four years (he only had four years of Wing Chun training, a year of mantis, and a couple of years of Filipino styles), he'd have a stronger set of fundamentals. But he didn't, and that made him a great theorist - ideal for teaching classes, building exercise equipment and writing books, but not much of a fighter.
I wouldn't give Bruce Lee odds in a fight against Muhammad Ali (Bruce himself said Ali would murder him). In a UFC event, he'd be ok in his weight class, but he wouldn't make the quarter finals against any of the top opposition there.
Again, I have to emphasize, I'm not knocking Bruce Lee in any way. I'm just being realistic here. His fighting concepts were groundbreaking, his speed spectacular, his training regimen top-notch, and his strength uncanny....back then. But martial arts have, on the whole, evolved past that, largely thanks to Lee. I have all the respect in the world for what he's given the martial arts world- "it's easy to look down on someone when you're standing on their shoulders". My own training incorporates understanding the five combat zones he discovered. But that doesn't give him a free pass as a combatant. The fact is, he'd get destroyed by most top fighters today.
And against Batman?
Lee takes 0/10