While preparing for his title defence against Joe Bugner in Malaysia in 1975, Muhammad Ali announced, "I will prove to the world that I am not only the greatest boxer of all time, I am the greatest martial artist." Then, before treating the kickboxer Davis Miller to a round of sparring, he declared, "You must be a fool to get in the ring with me. When I'm through, you gowna think you been whupped by Bruce Lee." Miller reported how "I bent to the right, tossed a jab toward his belt line, straightened, snapped a long, tentative front-kick to his head. I figured it was the first kick he'd ever had thrown at him, but he pulled away as easily as if he'd been dodging feet his entire life." In that brief encounter, Ali allowed Miller to get a few hits in before knocking him senseless with two punches.
Bruce Lee would no doubt fare better than the young Miller did against the Greatest, but the end result would probably be no different. Ali was 6ft 3in tall and weighed 236lb in his prime. Lee was 5ft 7in and just 135lb when he died. If Lee were a boxer he would be a lightweight nine divisions below Ali's heavyweight class. In regular boxing there is a limited degree of movement between the weight divisions.
The first advantage people think of is the martial artist's ability to use kicks as well as punches. In any contest of champions, Muhammad Ali would be allowed to kick too just as Bruce Lee would be allowed to punch but one presumes he would rely on his fists. The second advantage is Lee's dazzling speed though frames were cut from his fight scenes to make him appear even faster. Even so, his kicks could never be as fast as Ali's punches. This is no slight against the martial artist, but simply a reflection of human physiology and the laws of physics.
Even the fastest kicks are slow compared to punches, because they require more build-up and begin from a greater distance from their target. Punches can also be followed up with more of the same, whereas combination kicks are slower, more difficult to execute and usually lose power.
Furthermore, Ali would be used to dodging punches that were much faster than Lee's kicks. So to bring his kicks to bear, Lee would need to keep Ali at a distance. Assuming that the two are fighting in a ring of limited size, Lee would probably not be able to keep out of the boxer's way for long enough. Ali himself was extremely fast for a heavyweight, but even he couldn't avoid dozens of punches from the lumbering George Foreman (realising this, he even made it part of his game plan not to try to during their "Rumble in the Jungle"). Similarly, no matter how fast Lee might be, he could not realistically be expected to dodge every blow from Ali.
Now there's an arena in which the different fighting styles can be directly compared: the Ultimate Fighting Championship. Almost anything goes in mixed martial arts, or "cage fighting", except for eye-gouging and blows to the groin. Yet, contrary to the public's expectation when the sport began, kung fu masters have fared notably badly: even worse than pure boxers. The early years were dominated by grapplers, and even today fighters stand little chance unless they have excellent wrestling skills, as so many matches are settled on the ground, either with a submission hold or with one protagonist pinned down and pummelled unconscious.
The most successful mixed martial artist of recent times is Japan's Kazushi Sakuraba. Sakuraba came from professional (that is to say, staged) wrestling, but after his promoters went bust he talked his way into the Ultimate Fighting Championship's heavyweights-only Ultimate Japan tournament in 1997. He pretended that he weighed 203lb in order to qualify and, although he was really only 183lb, he defeated a 243lb ju-jitsu champion to score the first of several victories against bigger, stronger men. One of his smaller victims was the renowned Royce Gracie, who at 180lb himself once beat a 275lb heavyweight wrestler. Sakuraba's career and those of other champions in Ultimate Fighting appear to demonstrate that grappling skills are far more effective than other martial arts or boxing disciplines in overcoming a size disadvantage. The UFC has destroyed the mystique of martial arts by showing which techniques actually work. Kung fu is not one of them.
Bruce Lee had great respect for the skills of wrestlers, but he had different priorities and recognised that their techniques were not as photogenic as the looping kicks and acrobatics that movie-goers wanted to see. He realised that his moves were only for the camera, and that the flurries of hand trapping that he learned from wing chun kung fu would be of little use in a real fight. Unlike Ali, Lee never boasted that he could take on the world. He never fought in competitive tournaments either. To then say that Lee was the best martial arts fighter in the world let alone the best fighter per se would be like saying that the Harlem Globetrotters, basketball's answer to the WWE (World Wrestling Entertainment), are the world's best basketball team.
The more valid question is not whether Bruce Lee could beat Muhammad Ali, but how he would fare against Rocky Balboa...