Anakin, maybe. Darth Maul can be hit with a surprise attack and defeated.
For a more detailed analysis, Anakin is possibly faster, stronger, more powerful, and comparably skilled by virtue of being able to challenge Dooku, but aside from that, Maul probably has better dueling feats. Maul has better resilience, but I'm a bit unsure as to how much that would affect the fight. At this rate, I doubt any speed advantage he possesses would be better than negligible, and his strength advantage likely won't matter as well. Then we have Maul's unorthodox martial ability, which would give him the edge in physical traits.
So Anakin is more powerful, but not by a huge margin and I'd probably say that Maul wins 7/10, since he has the edge in other areas, which could be more important to a fight than raw power.
If this is based on the films?
Which judging by the OP it is. Being literate gives me the ability to decipher this from the description of the battle, as listed in the OP!
That said... Maul would win here, IMHO. His feats were more impressive at these points of the films.
IF comics and novels apply as well. Then this battle goes in the favor of Anakin Skywalker, for many reasons already listed. Honestly people... Can't you even read simple directions? It clearly states in the OP, that these are the film incarnations. So everything pertaining to comics or novels based on this factor would be moot.
@brynhyld: Because this is Comic Vine. Nothing in the OP stipulates movie versions, because, as I said, episode 1 is a time gauge, and refers to more than just the film. Unless "film versions only" is stipulated in the OP, it isn't. Once again, this is Comic Vine.
@brynhyld: No, we can use comics. Nobody mentioned anything about films being ignored. This debate is completely pointless. The EU has been rendered just as canon as the films now due to the fact that there is only one canon class, thanks to Disney's retcon. Nowhere did it ever state movie versions, and thus, we can use the EU. There is nothing wrong or difficult to understand about that.
And I still maintain that Maul would win in the EU, against AotC Anakin.
To be honest, Anakin is faster and stronger than both Obi-Wan and Qui-Gon (obviously not both at once), but then again, so is Maul. Anakin should be more skilled than them, though, considering how he did offer a challenge to Dooku. He just doesn't have as much experience.
Probably Maul, because of a slim edge in skill, greater physical versatility, greater martial skill, greater resiliency, and greater tactical versatility. I don't recall many impressive martial showings from Anakin up to AotC. Most of those are after that, during the events of the Clone Wars (not the series; the event), but then, that would imply Anakin had at least some skill up to AotC. Still, Anakin is minimally stronger and faster, though I doubt these edges would matter at all, and he is both noticeably more powerful and more versatile in the Force (especially combatively). Maul owning the most pertinent edge, skill, is what would carry him out. Anakin's edges in physical attributes are far too limited to be of worth, and Maul's martial skills mastery and physical versatility would cancel out Anakin's greater combative Force versatility and offensive Force power. That being said, they are close enough as duelists for Anakin to win at least a few rounds, and then there is always the minimal chance of Anakin entering a state of Dark Rage or having his potential elevate him to levels greater than his natural performance, which would also afford him the win for those rounds. He would still only win 3-4 rounds in my opinion.
@capitolpunishment: why take Darth Maul in his prime and not Anakin in his prime? when they are both in their prime, no way Darth Maul stands a chance. anakins knowledge of the force is far superior, including his telekinetic abilities. piloting abilities we can only assume also go to Anakin, as piloting was his strong point. light saber technique: Anakin was an equal match for a much stronger obi than the one maul faced. Anakin defeated dooku, who was arguably more powerful than maul. no way. Anakin wins, hands down.