Personally, I think Empire had the best lightsaber duel in the classic trilogy.
Luke didn't know Vader was his father, and he was trying to kill him. Downright scary and desperate of a fight!
In ROTJ, neither was trying to kill the other.
TPM had an awesome duel - especially with it going 3-way and then with Qui-Gon killed, Obi-Wan's intensity was incredible.
AOTC was great, if you count the duel as including all 4 players. However, it gives me mixed emotions:
It starts with Anakin wanting revenge on Dooku for all the Jedi that died trying to rescue them. That's a good cause, but Anakin moves carelessly and is down by Force lightning before you know it.
Obi-Wan moves cautiously, passionlessly, being careful because Dooku is so powerful.
Dooku has little motive, except to leave. If the younger Jedi had chickened out, he'd have just gotten on his ship and left. He really didn't care to see them die (or live). For some reason, he decides to kill Obi-Wan when Obi-Wan is down for the count.
Anakin gets back into the fight just then to save his master. It feels slightly half-hearted. We know Anakin's annoyed with Obi-Wan, and there's no love for his master shown by this point in the movie, after Shmi's death and Anakin's raging mad about it and looking to blame Obi-Wan. He seems he'll stop Dooku from killing him, just because he can. Because he doesn't want Dooku to take Obi-Wan from him. He doesn't want to fail. But the emotion that Obi-Wan showed concerning Qui-Gon's fate was much more passionate. Perhaps this was because Anakin was still in pain from the Force lightning, but I got the impression that whatever was on his mind, Anakin was really only thinking about himself.
This time he's more cautious when fighting Dooku, especially after he loses his second lightsaber (when fighting with 2).
Now when Yoda comes in, we get the impression that there was some resentment on Dooku's part for the way Yoda trained him. There is a past there, that's evident. But this is a show about power, and we're in awe of the Force and what it lets these two masters do, and have less invested in the characters. Yoda seems rather cynical about the whole conflict from the standpoint that it's just another effort he has to make and that Dooku's dug his own hole and the inexperienced like Anakin and Obi-Wan still need Yoda to take care of them. I don't have as much invested in Yoda's character in this fight, because he still wasn't a major character in the movie, though his larger role was great. But Yoda's emotional investment seems more like cynicism, than any amount of passion. But that's just me.
So I'd rank the lightsaber fights:
I think. I put ROTJ over AOTC for the reason that Luke was pushed to his darkest moment at this point, and he KNEW that was his father, and the fate that awaited his sister if he failed to do what he had to do there. It was more personal than "Don't let Dooku get away." It might be better than TPM for that reason, but it's hard to beat the flash in that battle. Again, in TPM there was vengeance for Qui-Gon at stake, which was more than there was to do in AOTC.
ANH is hard to classify. Obi-Wan was trying to get back to the ship. Vader already had a homing beacon on the Falcon. Why didn't he let Obi-Wan go, only to die when the Death Star blew up whatever base the fleeing ship led them to? There was anger and intolerance in that fight. He was angry at Obi-Wan and wanted to finally teach him a lesson. Obi-Wan's motivation was just to get back aboard the ship with Han and Luke. I suppose it's similar to Dooku's goals in AOTC, and Anakin being angry (again of course) with Dooku for the Jedi that died. In one film he's angry about injustice to others (AOTC) and by ANH he's upset about everything that has gone wrong in his personal life and looking to take it out on the one it was most convenient for him to blame. Like I said, he could have let Obi-Wan go to Yavin, if he thought he could blast them all out of existence and that's what the tracker on the Falcon was there for. Like Leia said, the whole escape was a set up. They made it "easy." Though it certainly didn't look that way. I suppose it was only easy AFTER the Falcon left the Death Star - 4 TIEs as opposed to 30???
Hmmm. Looking at the story, ANH's lightsaber duel might have been better than AOTC? But Clones' with Yoda's stint fighting in it, kind of pulls its weight too.