Here's the script between Luke and Vader: ROTJ
Luke and Vader are engaged in a man-to-man duel of lightsabers
even more vicious then the battle on Bespin. But the young Jedi
has grown stronger in the interim, and now the advantage shifts
to him. Vader is forced back, losing his balance, and is knocked
down the stairs. Luke stands at the top of the stairs, ready to
attack.
Luke ignites his lightsaber and screams in anger, rushing at his
father with a frenzy we have not seen before. Sparks fly as Luke
and Vader fight in the cramped area. Luke's hatred forces Vader
to retreat out of the low area and across a bridge overlooking a
vast elevator shaft. Each stroke of Luke's sword drives his
father further toward defeat.
The Dark Lord is knocked to his knees, and as he raises his sword
to block another onslaught, Luke slashes Vader's right hand off
at the wrist, causing metal and electronic parts to fly from the
mechanical stump. Vader's sword clatters uselessly away, over the
edge of the platform and into the bottomless shaft below. Luke
moves over Vader and holds the blade of his sword to the Dark
Lord's throat. The Emperor watches with uncontrollable, pleased
agitation.
now the advantage shifts
to him. Vader is forced back; Luke now has the advantage and forced Vader back. And Vader was willing to kill Luke or else he wouldn't have threw his lightsaber at him or he wouldn't have watched Luke suffer at the hands of Palpatine.
And about Dooku's lighting: Yoda didn't struggle at all to block it neither did Obi-Wan. Mace and Yoda struggled to hold back Palpatine's.