Pretty even they both managed to cut off each others hand.

Pretty sure Luke Skywalker wins the duel depicted from the movies.

Throughout all Canon (not just the Star Wars films featuring Luke), Luke is far, far more superior. Actually, it's canon that Luke Skywalker is the strongest force user, out of both the Sith and the Jedi.

EDIT: Skip to the bottom for the tl;dr of this nerd essay.

As a personal note to the creator of this debate, it's possible to capitalize and put spaces in between the descriptions for each side's position in the debate. You don't have to fuse words together and not capitalize proper nouns.

But, onto my argument:

If we are assuming it's an even fight, we have to take both of them at the height of their power in this hypothetical match up. If we take both of them at the height of their power, it's a fairly even match; in Return of the Jedi, Darth Vader is nowhere near the height of his strength by any means, and Luke is freshly on the rise as the only traditional Jedi Guardian in the entire galaxy (well, other then bullshit stuff that breaks the movie and primary book canon, that is).

So of course, Return of the Jedi wasn't a fair fight in regards to the duel between Darth Vader and Luke Skywalker. Darth Vader had more experience in the duel, and fear on his side, but Luke was still more powerful, even if he or the audience did not know it.

This is because, when Darth Vader was turned into a cyborg, he lost a portion of his ability to use the Force. BUT, he is still the Chosen One, and thus, as an educated Jedi/Sith Lord, literally has the power to practically be invincible and unstoppable, even if he had to be grafted with a large amount of synthskin and had all his forelimbs cybernetically replaced.

In the expanded lore, however, the Skywalker bloodline is considered is the 'Legacy Family,' and Darth Vader, as the Chosen One, is it's 'patriarch'. The lore is somewhat changed this way from the movies to account for Luke and Leia also being strong in the Force, more so then a normal person, but not as much as Darth Vader.

With that established, we know that at base, Luke and Vader are genetically unequal in the usage of the Force. But to be realistic, we have to take into account periods of their lives when considering the heights of their strength.

Darth Vader's height of strength was more or less the first 10 years he spent as a Sith Lord, probably somewhere 5 years or so into it. It wasn't closely around the time when he first turned, nor anytime during the Original Trilogy. This is because, even though Darth Vader wasn't a cyborg when he first turned, he was still newly turned and had no experience with how to use the dark side of the Force. Thus, he was basically an untrained Dark Jedi, which required experience with using the dark side of the Force to be powerful, in the lore. In other words, even though he was extremely powerful and not limited in his ability to use the Force, he didn't know how to use the dark side properly, and therefore had a handicap. This handicap of inexperience is why he was defeated early on by Obi-Wan Kenobi.

After Darth Vader was recuperated as a cyborg, this was when his power started quickly growing towards it's critical mass. Even though Darth Vader now had a new handicap placed upon his ability to use the Force, he acquired a tradeoff that, when coupled with a mastery of the dark side, ultimately made him deadlier then before he was a cyborg. As demonstrated with General Grievous in the original 'Clone Wars' cartoon miniseries, cyborgs in Star Wars can use the physical upgrades from being mechanical to give them nearly Force-trained like physical prowess. (The reason Grievous and Vader did not demonstrate such prowess in their respective episodes is because of physical factors that happened off-screen)

With this said, in Vader's earlier years as a Sith Lord and cyborg, his slight handicap over his force usage was easily overcome by the fact that he was the Chosen One, and that he was at that point very and properly learned in the Dark Side. With that limitation overcome by those factors, Darth Vader also had an additional advantage: he was cybernetic enough to be super-human at physical base, but not so cybernetic that he channeled the Force significantly less then he could before.

This, altogether, is why his younger years into being a Sith Lord put him at his most powerful, before he quickly began to decline in power when he slowly turned into a middle-aged man. He was a cybernetic death machine with his lightsaber, unmitigated dark side Force-use, and significant physical augmentations.

Now let's talk about Luke. As a Skywalker, Luke has a genetic boon to his ability to use the Force; not as great as Vader, but still one. If we go and look at Luke's height of power, this would actually be the opposite of Vader as it would be when Luke is old(er) instead of young(er). This is because of the nature of the Force. The dark side grants tremendous power, but it ages you very keenly, and in Darth Vader's case, aged him to the point of being much physically weaker then a normal cyborg. The light side, inversely, grants a moderate amount of power, but ages you very mildly, even allowing you to be physically more capable when elderly then other people whom are a proportional age.

Later in Luke's life when he was nearing middle-age, he at that point was probably at his critical mass of power. He was the Jedi Master of the New Jedi Order during the Vong War, the second Galactic Civil War, and several other conflicts. During these periods Luke not only mastered his ability to use his lightsaber, but he also reached the highest point of force usage he could possibly muster. In fact, by the end of the Vong War, it was actually established in the lore that the Force did not truly have multiple sides, and it only manifested as light or dark based upon the person using it. The result was that Luke Skywalker, at the height of his power, was a relatively powerful warrior, but he had the capability to use every Force technique, 'dark' or 'light', in combat without any temptations that would otherwise lead him to, or make him even think of, the dark side.

So, Luke at his highest state of power wasn't primarily as a warrior, but, say, a great wizard. A sage. He relentlessly would channel the Force as if he were Gandalf the White in Lord of the Rings, and resort to his lightsaber only unless it was necessary in the fight he was participating in. He was like Emperor Palpatine, except a Jedi and not hideous or evil.

With that established, pitting Luke Skywalker and Darth Vader against one another in their prime of power would likely result in Luke as the victor.

I surmise this for a few reasons (- is a negative towards the conclusion, + is a positive):

- Darth Vader's slight handicap at channeling the Force caused him to be more of a Sith warrior then an acolyte. He almost always got up close and personal, and only supplemented his combat with non-physically-augmenting Force powers. Even though Luke masterfully knew how to use his lightsaber, it wasn't his focus, meaning Vader's style of focusing on close combat has a good chance of breaching Luke's defense.

- Luke can think quickly in the fray, but Vader can think faster. The trained recklessness involved in Sith warrior melee combat would have it be that speed outmaneuvers cleverness. That, coupled with Vader's cybernetic augmentations, makes Luke offensively outmatched in melee.

+ Darth Vader and Luke are both experienced in combat, the difference being that Luke, nonetheless, keeps an objective tone with his strategy. He is experienced in fighting powerful melee fighters just as much as Darth Vader is experienced in fighting powerful defense fighters, but Luke can make better decisions that go towards his victory. Even if said decisions are slower then Darth Vader's, they still have a significantly higher chance of being the right ones, which could easily overturn Vader's speed advantage.

+ Luke Skywalker's melee defenses are balanced and stalwart. He uses the lightsaber combat forms of Soresu, Ataru, and Djem So. In other words, Luke's entire melee style focuses primarily upon some form of direct or indirect defense. That, coupled with his experience and type of strategy for fighting makes him probably good at, or at lease capable of, withstanding an impetuous melee opponent without totally loosing the opportunity to use his more powerful Force powers.

+ Finally, Luke's sort of dueling style is ultimately a detriment to Vader, because Vader is a cyborg. This isn't because droids or mechanics are vulnerable to the Force inherently, it's that flesh is inherently defended against the Force. Even a normal individual who is not trained in the Force is inherently less effected by it then a droid, because the Force flows through living things. Since Vader is a cyborg, even though he is the Chosen One and extremely powerful in the Force, a great portion of his actual body composition is significantly undefended against the Force. When Vader channels the Force, it does not channel through his limbs from the inside. When a non-cyborg Jedi channels the Force, it flows through their entire body. With this pointed out, Luke Skywalker at his height is powerful not because he is a warrior, but because he is sagacious and a Force sorcerer. Any opportunity he has to strike at Darth Vader with a power is proportionally more damaging then if Darth Vader were not a cyborg. It's essentially the exact reason that Darth Vader dies at the end of the Return of the Jedi; the Emperor doesn't even focus his Force lightning at Vader, but mere backlash from the lightning completely ruined Vader's cybernetics, which were apart of his body and were keeping him alive.

In conclusion, Darth Vader is extremely powerful, and if some sort of fight simulator like Deadlist Warrior were to take Darth Vader at his most powerful, and Luke Skywalker at his most powerful, calculated all of their combined strategies, defenses, and offenses, Darth Vader would certainly have SOME wins. He is, after all, Darth Vader, the Chosen One, Dark Lord of the Sith, the most powerful Force-user to ever exist in his era. But ultimately, I think Luke would win more then 50% of the time, simply because, even though Darth Vader's cybernetics are actually an advantage in every battle, they are also a disadvantage against Luke Skywalker's mastery of offensive Force-powers and melee defense.

If these two were to have 5 hypothetical battles, I'd say it would go like this:

1. Vader relentlessly shatters Luke's melee defense with an unmitigated onslaught. Vader wins.

2. Luke's defense holds out long enough for him to get in a decisive counter-attack. Luke wins.

3. Vader is able to use his greater speed to get in a decisive attack before Luke can counter. Vader wins.

4. Vader wastes his greater speed on a risky attack that allows Luke an opening. Luke wins.

5. Luke risks an uncertain moment to use a Force power on Vader. Vader looses the benefit of his cybernetic augmentation and is no longer faster and stronger then Luke. Luke wins.

Vader: 2, Luke: 3

Tl;dr: I think Luke Skywalker is the more-often winner of an evenly-matched duel with Darth Vader.