Battle of the Heroes - Part 1
In the shooting script the duel was originally written as an uninterrupted sequence with the possible exception of some intercutting to the droids trying to move Padme's body into the ship. During editing this was changed and the duel was intercut with the Yoda/Sidious duel instead.
Some small bits of footage were dropped because of this, mainly transitional sections where Obi-Wan and Vader moved from one location to another since those were probably good spots to cut back to the other fight.
The Duel runs pretty smoothly overall but there is some more significant footage cut later on in the duel as well as some dialogue.
The Main Control Center
After Obi-Wan and Anakin fight their way into the Control Center there is some dialogue in the script which was omitted.
INT. MUSTAFAR - MAIN CONTROL CENTER - DAY
And a bit later when they've moved back into the control center after fighting in the conference room...
Don't make me destroy you, Master. You're no match for the dark side.
I've heard that before, Anakin... but I never thought I'd hear it from you.
The flaw of power is arrogance.
You hesitate... the flaw of compassion.
The Conference Room
This segment in the movie begins in mid-action as Anakin grabs Obi-Wan and begins choking him.
There was a beginning to this section that was cut. Obi-Wan was supposed to get a hold of Anakin's lightsaber somehow and use both swords briefly before Anakin choked him.
This is why Obi-Wan is holding Anakin's lightsaber in his right hand in the shots where Anakin is strangling him.
There is still a bit of an oddity in this sequence however as in one shot Obi-Wan is holding his own saber hilt in his right hand but in the shots before and after that it's Anakin's hilt he's holding.
So it's either a small continuity error or there's more to this that's missing. I imagine the ceiling was probably damaged at some point in this omitted footage as well which would explain why it's showering with sparks during the rest of the segment.
George Lucas mentions this cut segment during the audio commentary on the DVD.
Nick Gillard also mentioned that Obi-Wan would use two lightsabers briefly in one of his Hyperspace chats before the film came out.
-Pic #1: From Star Wars Insider #71. (Nootice Obi-Wan's saber hilt lying on the table.
-Pic #2: From ROTS Visual Dictionary. A completed but omitted shot.
-Pic #3-4: From ROTS DVD "It's All For RReal" documentary. Stuntman Michael Byrne rehearsing the duel. (Notice he's holding two sabers.)
-Pic #5: Screengrab comparison showing tthe switching of saber hilts in Obi-Wan's hand.
Balcony Outside the Control Center
There were a couple small bits of swordplay cut from this section on the balcony outsite the control center. The first deleted bit was before Anakin kicks Obi-Wan. It featured a cool move where Obi-Wan did a stabbing lunge to Anakin's head which Anakin very nonchalantly dodged by just moving his head to the side. This footage is shown many times in various documentaries but you can get a good look at the rehearsal in It's All For Real: The Stunts of EpIII" on the ROTS DVD and also see a bit of the filming at the beginning of the Making of Episode III Videogame doc on the OT DVD Bonus disc. The first shot below (from SW Insider #81) with completed effects is from this omitted segment.
The second bit cut from this section is after Anakin kicks Obi-Wan in the face. This footage was cropped off to intercut back to the Yoda/Sidious fight. After the kick, the fight would have continued to the end of the balcony where Obi-Wan jumps over the railing and onto the pipes over the lava. Again, the beginning of the Making of Episode III Videogame on the OT DVD Bonus disc shows a bit of this footage. This part is very short and only consists of a few moves so it's not a big loss.
Battle of the Heroes - Part 2
-Illustrated Screenplay E-Book.
-ROTS Making of book.
-ROTS Visual Dictionary.
-Star Wars Insider #76 & #81.
-ROTS DVD: "It's All For Real", "Within A Minute" docs, Theatrical trailer.
-OT DVD Bonus disc: Making of EpIII videogame.