It's already been done, but I feel like saying it:
Anakin would probably have a harder time with Maul than Dooku. No, I don't think that Maul>>>>Dooku. In Star Wars, A being greater than B and B being greater than C rarely means that A is greater than C. Anakin would have a harder time with Maul due simply to the way they fight.
Dooku is older, obviously. He fights with a style revolving highly around finesse. He relies on a combination quick, highly accurate strikes to disable his opponents (As shown in AotC when fighting Obi-Wan), and Force techniques (As shown when fighting Obi-Wan in RotS). However, seeing as he's older now, he lacks the brute power that certain others such as Anakin and Maul. When faced with someone who has a lot of brute power but not nearly enough skill, such as Anakin in AotC, this isn't a problem. But against opponents like Maul or RotS Anakin who have not only the brute strength, but more than enough skill, he's at a severe disadvantage. Especially considering that both Anakin and Maul are not only highly skilled with sabers, but that they're pretty advanced in terms of hand-to-hand and some grappling abilities.
This means that not only can they overpower a style like Dooku's by putting raw power behind lightsaber strikes (As Anakin tends to do), but he's very poorly defended against simple hand-to-hand attacks. This is clearly shown when Anakin (While in a saber lock, IIRC) grabs his wrists, pulls him forward, and twirls his saber to cut off his hands. He spent time overpowering Dooku with the saber, and finished it by using brute strength, only using his saber to cut off Dooku's hands.
Now, against Maul, this simply wouldn't be as effective. Dooku was physically weaker than Anakin, and as such Anakin had a rather easy time overpowering him with raw physical strength. Maul, on the other hand, is probably just as strong as Anakin (Excluding Anakin's mechanical arm), and as such Anakin wouldn't be able to simply overpower him. Likewise, while Maul might be able to physically overpower Dooku, he couldn't do so with Anakin. With that in mind, it comes down to a matter of saber skill, and Force strength/skill. They both display similar types of Force abilities (Push, grab, etc, etc.), but Anakin has the advantage in power here. Both of them also seem to use rather aggressive saber styles (IIRC, Anakin uses Djem So and Maul uses Juyo style slightly altered for a double-bladed saber).
So in the end, my vote goes towards this:
Force only: Anakin pwns. They haven't displayed too many abilities, but Anakin has much more raw power.
Saber only: It could go either way. Both of them use aggressive styles, both of them have a lot of raw physical strength, and both of them are highly skilled in their styles.
All out: Anakin owns, but probably not quite as easily as he would if it was using the Force only.