It comes down to power vs. wits.
Scientists have created a more accurate Neanderthal reconstruction, based on a nearly complete skeleton discovered in France more than 100 years ago. The La Ferrassie Neanderthal man was short but stocky. If a modern man came nose-to-nose with a Neanderthal, could he take him in a fight?
Possibly. A Neanderthal would have a clear power advantage over his Homo sapiens opponent. Many of the recovered Neanderthals had Popeye forearms, possibly the result of a life spent stabbing woolly mammoths and dismantling their carcasses. A Neanderthal had a wider pelvis and lower center of gravity than Homo sapiens, which would have made him a powerful grappler.
That doesn't mean, however, that we would be an easy kill. In general, we would have a longer reach and more stamina. We could deploy these advantages to maximum effect using our superior wits.
The image of Neanderthal as a squat, chiseled brute is sometimes overstated. Based on the number of known specimens, it appears that males averaged 5 feet 5, only 2 inches shorter than the average Chinese man today and 4 inches shorter than the average American man.
It would also depend on training. A trained modern fighter would know exactly where to strike the Neanderthal for maximum damage, giving him a tremendous advantage. On the other hand, the human brain can work against us in combat. Many animals continue to struggle long after they are shot, for example, while humans tend to collapse immediately under the psychological stress of being wounded.
When it comes to fighting for our lives, we are sometimes too smart for our own good.