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This topic has been touch on before in different topics.

Quotes from ROTJ: http://www.imdb.com/title/tt0086190/quotes

Yoda: No more training do you require. Already know you, that which you need.
Luke: Then I am a Jedi.
Yoda: No. Not yet. One thing remains. Vader. You must confront Vader. Then, only then, a Jedi will you be. And confront him you will.

Yoda: Remember, a Jedi's strength flows from the Force. But beware. Anger, fear, aggression. The dark side are they. Once you start down the dark path, forever will it dominate your destiny. Luke... Luke... do not... do not underestimate the powers of the Emperor or suffer your father's fate you will. Luke, when gone am I... the last of the Jedi will you be. Luke, the Force runs strong in your family. Pass on what you have learned, Luke. There is... another... Sky... walker.

Darth Vader: I see you have constructed a new light saber. Your skills are complete. Indeed you are powerful as the Emperor has foreseen.

Darth Vader: Give yourself to the Dark Side. It is the only way you can save your friends. Yes, your thoughts betray you. Your feelings for them are strong. Especially for... sister. So, you have a twin sister. Your feelings have now betrayed her, too. Obi-Wan was wise to hide her from me. Now his failure is complete. If you will not turn to the Dark Side... then perhaps she will...

Since the movie is the highest form of canon, question is was Luke really strong enough in force and saber skills to defeat Vader?

^Only when Luke gives into his anger does he truly pose a threat to Vader, which he did the entire the fight, the only time he wasn't was when he disengaged his lightsaber and ran/hide then when Vader taunted him, he flipped again.

I've often considered Yoda's line about "no more training do you require" to mean not skill with the Force or lightsaber, but that nothing Yoda can teach him now will prepare him for what he'll face. Luke at this point will either get it, or he won't--he'll reject the Dark Side, or he won't.

As the movie makes no mention of what level Luke's skills are at, we can freely leave it to the EU to establish the details without fear of contradicting the movies. He used the Dark Side to defeat Vader, and he rejected outright a minute later. No doubt this sudden reversal and his subsequent line of "...Jedi, like my father before me" spurred Vader's decision.

When fighting Vader on the Death Star 2, Luke showed a trait that Cade has...touching the dark side to increase his saber and force skill, when he's not quite at a level to do it naturally.

And, like Cade, is able to focus himself to not take his angre beyond the fight...straight after besting Vader and realising that they are one and the same, he turns to Palpatine and is as calm as a butterfly. No freaking out, no lashing out... just calm, collected nature.

There are some good points made here which I agree with for the most part. One thing I would like to mention is that the statement about Luke training was made not only by Yoda but by Vader himself. This would mean that Luke would have a least reach a level in which he would be able to defeat Vader.

Also different from there previous fight is that Vader did not use the force to show his superiority. There could be two reasons for this:
1. It would not work on Luke due to his level of power thus attained or mastery of the force.
2. Vader never got a chance to use it.

Originally posted by Kotor3

Also different from there previous fight is that Vader did not use the force to show his superiority. There could be two reasons for this:
1. It would not work on Luke due to his level of power thus attained or mastery of the force.
2. Vader never got a chance to use it.

3. Vader held back the entire time according to luke.

And your reason 1 sounds stupid, if thats the case why are people like sidious nad galen whom are close in power are able to beat his outher up?

Seriously how many damn threads are you going to make about the same topic over the course of a few months? Get over it.

Vader "holding back" went as far as him not using the Force to cave in Luke's skull. The novelization makes it clear that he was willing to kill his son.

" anger was layered, now - he did not want to win if the boy was not battling to the fullest. But if winning meant he had to kill a boy who wouldn't fight... then he could do that, too."