Things are changing fast ....
This is a Stop Motion Battle between Count Dookusun (or Nedooku ) and Anakin Steemwalker from earlier this morning.
Relax ... It's Just a flesh wound .... Anakin is OK. This is a New Movie.
Happening Live.
At Wookieepedia I found the following:
Dooku was a respected instructor in the Jedi Temple and one of the most renowned swordsmen in the galaxy. Only Masters Yoda and Mace Windu were considered his equals.
When it comes to lightsaber combat mastery one finds regularly these three names, sometimes alongside Darth Sidious, but not that of Anakin Skywalker or Darth Vader. Examples:
Mace Windu was a formidable warrior and generally considered one of the greatest swordsmen ever produced by the Jedi Order [...]. Even without his unique fighting style, it is said that only his one-time friend, Dooku, and the venerable Grand Master Yoda could outspar him.
Yoda was a master of lightsaber combat, one of the greatest duelists of all time. It was said that only Mace Windu, Count Dooku and Palpatine were able to fight with him on equal terms.
So how could Anakin defeat Count Dooku so easily at the beginning of The Revenge of the Sith?
This Question contains some good points but I guess it can't be only a matter of fighting styles as Dooku's "Makashi" is a special dueling style and he had good knowledge of the other styles too.
Maybe Dooku's age played a role but then again when the force is your ally this shouldn't matter too much (see Yoda).