I am going to have to agree with demigawd....bruce lee was an awesome film actor, but he was not much of a fighter. Most of his life he was frustrated with his style and though in supreme physical condition, not benching 700lbs like someone said though, he was pretty much a beginner as far as real skills go. He looks amazing to the untrained but to an experienced fighter he is very basic.
Back in the '60s, there was a Batman episode where Batman (Adam West) squared off against Green Hornet (-?-) and Robin (Burt--flesh-colored-tights--Ward) squared off against Kato (Bruce Lee, not the OJ Ditz). While Batman and Hornet pretty much kept it to fisticuffs, Kato was literally kicking Robin's butt all over the gosh-darn room. Another few minutes, and he woulda been on Batman's ass.
That aside, and trying to compare real to fake, all else being equal, I would be inclined to give this to Lee first bout, cuz being smaller he'd be faster and more maneuverable. But being the fast learner and tactician Batman is, I see him trumping Lee in the long run.