I love them all equally, which is why I chose all three. It would be a cardinal sin in my honest opinion to only select one.
All three are masterpieces.
I will say Return of the King is by far, the most emotional out of the trilogy and has a lot of scenes that are very moving, powerful, beautiful, and contain some great acting.
My favorite scene or maybe I should say scenes in Return of the King are as follows:
1. After Frodo is stabbed by Shelob, Sam appears and fights Shelob thus showing his bravery and loyalty to Frodo once again. I love the end quote as he is holding a comatose Frodo in his arms, "Don't go where I can't follow."
2. The Charge of the Rohirrim
3. Aragorn, Gimli, and Legolas entering into the Paths of the Dead.
4. Sam holding Frodo on Mount Doom. The music is slowly building and the acting between Astin and Wood is amazing. Why Astin didn't get nominated for best supporting actor is beyond me. Seriously, who didn't tear up or cry when Sam says "Come on Mr. Frodo! I can't carry it for you! But I can carry you!"
5. The Grey Havens.
I seriously had a hard time holding back the tears with Frodo leaving. I knew it would happen since I read the book, however, it was still beautiful to see on the big screen.
Obviously there are more brilliant scenes in Return of the King. Those are the ones that stand out to me the most, but as a whole the film is brilliant and is a masterpiece.