What a contrast this duel has to the first encounter between Luke and Darth Vader. In Episode V, Luke was a brash, callow acolyte in the Jedi arts, determined to prove himself and avenge the deaths of Obi-Wan and (he supposes) his father. He is the aggressor, refusing to back down even when it's obvious he is terribly outmatched. Vader goads him, tests him, encourages his anger, and calls him to the Dark Side. It's only when all other hope is gone that Luke learns to let go and fall to his apparent doom rather than embracing aggression and despair.
Now, having learned some very hard lessons, he has become a true disciple of Jedi pacifism and compassion. In a striking reversal, he is the one urging Vader to change sides. Calling him back to the light. Insisting that he still senses good in his father. Continually lowering his weapon and refusing to fight. Not that he's entirely passive. He did briefly succumb to anger in his attempted attack on the Emperor, and it's probably survival instinct that has him reigniting his saber to defend himself whenever Vader aggresses. But there's no question that Vader is the primary aggressor.
He does not, however, urge Luke to join him this time. That is purely the Emperor's realm now. The power play has shifted considerably since Vader schemed to make Luke his apprentice and overthrow Palpatine. Vader might have recognized, on some level, that he has little chance of becoming a master with Luke as his apprentice. His words and his tone are deeply fatalistic and grim. The Emperor is gleeful, confident of his impending victory. Vader has no such pleasure. He fulfills his duty as a Sith apprentice with dreary inevitability.
But Luke seeks a role beyond serving as a pawn in Sithly power plays. His soul is not the only one that matters. He seeks to reclaim his father's.
"I feel the good in you, the conflict."
"There is no conflict."
"You couldn't bring yourself to kill me before, and I don't believe you'll destroy me now."
"You underestimate the power of the Dark Side. If you will not fight, then you will meet your destiny."

Followed by a rare, and effective, case of using a lightsaber as a projectile. Luke tumbles from the catwalk and goes into hiding. But this was hardly a victory for Vader. His son continues to resist the power of aggression and hate. After twenty years serving the Dark Side, Vader might have come to believe such a thing was impossible. That everyone must eventually succumb to the superior, all-encompassing power of darkness.
Imagine audiences on a first viewing of these films. Just as we might have doubted the notion that Luke could fall to the Dark Side when it was first introduced, now we might believe him straight-up delusional for believing there is good left in Darth Vader. Luke claims to sense the good in him, but we have no way of knowing if it's a genuine insight or simply wishful thinking. We're left guessing till the very end, even through a moment when Luke's own soul will teeter on the brink.
Next time, the battle of souls continues...