It's not as easy or simple as "who beats who".
You're taking the two deadliest Spartans in history and pitting them against each other. A lot of people are pointing to Six being a Spartan-III and using their inferior augmentations, experience, and armor to claim an easy victory for the Chief. But the fact of the matter is Six is the only other Spartan to be labelled "Hyper-Lethal"; what's more is that, despite the fact that Spartan-IIIs are designed to work in teams, Six is the exact opposite: they work better as a lone wolf. These two little details are actually very important indications of exactly how skilled Six actually is. I dare say Noble Six is probably the only Spartan-III that could stand toe-to-toe against a Spartan-II and be able to hold their own, even the Chief, because Six displays the skill of a Spartan-II in spite of being a Spartan-III.
Therefor I say who would win in a fight between the Chief and Six would entirely depend on the factors surrounding this hypothetical fight: environment, equipment, weapons, if Chief has Cortana with him, vehicles, etc. I would say that Six makes up for their status as an inferior Spartan-III by being just as skilled as Chief - if not more so. Thus, I'm reluctant to hand victory to the Chief outright. I think the context of this fight is what decides who wins rather the participants. Chief is the better weapon, but Six is the better soldier, so I'm calling it a toss-up determined by what they do or do not have because, frankly, Six has all the makings of a Spartan-II and had they been younger and on Halsey's list, I guarantee you Six would have definitely been superior to the Chief in every aspect because I am of the opinion that even s a Spartan-III Six is at least on equal footing with the Chief in terms of pure skill.
They also manage pretty damn well without "luck", too.