Dueling Abilities:
Mace Windu
Mace Windu was easily one of the top 5 duelists in Star Wars history, on par with the likes of Dooku. Mace Windu created his own lightsaber form called Vapaad. He was the only one to use it without falling to the dark side.
Yoda considers only Windu capable of fighting equally with Dooku
The Count's blade was quick as a viper striking. Among the other Jedi, perhaps only Mace Windu would have been his equal on neutral ground: but here on Vjun, steeped in the dark side, his bladework was malice made visible—wickedness cut in red light.
-Source: Yoda: Dark Rendezvous
Windu's mastery of the blade was so great he could deflect blaster bolts without even looking
At the time of Attack of the Clones, Windu is second only to Yoda.
Nick Gillard : We didn't see Mace fighting yet, but we know that he is second only to Yoda...
-Source : Star Wars Episode II: Action Featurette
Mace was said to have been one of the best duelists in Jedi history.
Which would leave Mace and Agen Kolar—both among the greatest bladesbeings the Jedi Order had ever produced—here on Coruscant in case Sidious did indeed take this opportunity to make a dramatic move.
-Source: Revenge of the Sith
His skills were said to have been unmatched.
This is the moment that defines Mace Windu.
Not his countless victories in battles, nor the numberless battles his diplomacy has avoided. Not his penetrating intellect, or his talents with the Force, or his unmatched skills with the lightsaber.
-Source: Revenge of the Sith
Mace has sparred evenly with Saesee Tin, one of the best duelists in the order. Though it was a spar, so neither fighter were going full out. If they were, Windu would win convincingly.
Mace stalemates with Sora Bulq, though it appears he's putting little effort into the fight.
Mace has easily defended against Quinlan Vos, showing no real effort.
Windu has also defeated Asajj Ventress, forcing her to flee. Ventress is someone who has given Obi-Wan Kenobi and Anakin Skywalker trouble.
Windu has once engaged Dooku, though none seemed to get an advantage over the other.
Anakin Skywalker
Anakin Skywalker was likely the best Djem-So practitioner of all time.
Dooku claimed he was the best he'd ever seen.
Skywalker's Shien ready-stance had been a ruse, as had his Ataru gymnastics; the boy was a Djem So stylist, and as fine a one as Dooku had ever seen. His own elegant Makashi simply did not generate the kinetic power to meet Djem So head-to-head. Especially not while also defending against a second attacker.
-Source: Revenge of the Sith
Here Anakin bests Dooku in lightsaber combat, until Dooku resorts to his force lightning.
This could be partly because of Makashi's weakness to Djem-So.
Again, Dooku is defeated by a rage amped Anakin.
https://www.youtube.com/watch?v=eYT3ctPuVRw
He's even matched Ventress and Dooku at once for a time.
During a sparring session he fights evenly with Obi-Wan Kenobi
Anakin has also easily defeated Jedi Battlemaster Cin Drallig
Stone-faced, Obi-Wan watched younglings run into the room, fleeing a storm of blasterfire; he watched Cin Drallig and a pair of teenage Padawans—was that Whie, the boy Yoda had brought to Vjun?—backing into the scene, blades whirling, cutting down the advancing clone troopers with deflected bolts.
He watched a lightsaber blade flick into the shot, cutting down first one Padawan, then the other. He watched the brisk stride of a caped figure who hacked through Drallig's shoulder, then stood aside as the old Troll fell dying to let the rest of the clones blast the children to shreds.
Obi-Wan's expression never flickered. He opened himself to what he was about to see; he was prepared, and centered, and trusting in the Force, and yet... Then the caped man turned to meet a cloaked figure behind him, and he was—
He was—
Obi-Wan, staring, wished that he had the strength to rip his eyes out of his head. But even blind, he would see this forever. He would see his friend, his student, his brother, turn and kneel in front of a black-cloaked Lord of the Sith.
- Source: Revenge of the Sith
He was also a better fighter than Obi-Wan
The ease with which Kenobi had taken command of the situation was frightening. More frightening was the fact that of the two, Skywalker was reportedly the greater warrior.
- Source: Revenge of the Sith
Summary
These two are nearly equal as duelists, however I do think one gets a slight edge. In terms of technical skill, Windu outclasses Anakin for sure, however his raw talent and potential nearly negates this entirely. I am more impressed of his handling of Dooku and Ventress.
Dueling Abilities = Anakin Skywalker
Force Abilities:
Mace Windu
Mace Windu was an incredibly powerful Jedi, said to have been the second most powerful Jedi on the council.
He seems to be second most powerful jedi on the that council, next to Yoda.
-Source : Insider #55
He's casually dismissed Sora Bulq and Quinlan Vos with his use of the force.
He's thrown a droid 3 kilometres
He's exploded Speeders with casual ease
collapsed bridges with similar ease
Destroyed droids with impressive master and command over the force.
Showing a great amount of power, Windu has pushed an AT-TE off a cliff.
He's also crushed Grievous with his use of the force.
This is impressive, because Grievous has shown he can tank missiles and explosions like they were nothing.
Anakin Skywalker
Anakin Skywalker had the potential to become the most powerful force wielder ever, even better than Grandmaster Luke Skywalker and Emperor Sidious. Sadly, he never reached that potential.
Still, Anakin remained an incredibly force wielder with monstrous power.
He's breached Dooku's force wall several times
As well as dominated other force users such as Bariss Offee and Ventress.
He's manipulated an entire pod to go towards a sun
He's destroyed a giant spider droid
He's moved a CIS Dreadnaught way before his prime
Similar to Windu, he's casually dismissed droids before his prime.
Wrapped Ventress in wires
Summary
At this point I'd say the two are around equal in terms of raw power, however Windu simply has better mastery and command over the force.
Force Abilities = Mace Windu
Physical Abilities:
Mace Windu
Windu has moved so fast he seems to have phased through a blaster bolt.
He's also casually smashed through Durasteel
Most impressively, he breaks out of the hold of a Gundark, creatures with monstrous strength
Anakin Skywalker
Anakin has casually dominated the likes of Ventress and Bariss Offee with his strength alone.
Anakin's strength was compared to the likes of a meteor, though this is likely exaggeration
Skywalker was all over him. The shining blue lightsaber whirled and spat and every overhand chop crashed against Dooku's defense with the unstoppable power of a meteor strike; the Sith Lord spent lavishly of his reserve of the Force merely to meet these attacks without being cut in half, and Skywalker—Skywalker was getting stronger.
-Source: Revenge of the Sith
He's also survived a beating by Durge and kept on fighting.
Summary
I think Windu has a slight advantage here. Anakin is more durable, but I think Windu is faster and stronger.
Windu has gotten out of the grip of a Gundark, something Anakin failed to do.
Physical Abilities = Mace Windu
Conclusion:
This is so close. When making this post I kept going back on forth on who'd win.
The fight would mainly be a lightsaber duel. Even though I said Anakin gets an advantage for his dueling abilities, I do think Windu can edge out Anakin here, because of Vaapad. As Anakin gets more and more angry and frustrated, the stronger Windu would get. One half of Vaapad is to accept your opponents fury and turn it against them in one half of a superconducting loop, the other half is to accept ones own inner darkness and let it power you. That's why every Jedi who tried to use the form fell to the dark side. Depa Billaba, Sora Bulq, Quinlan Vos.....but not Mace Windu. Mace Windu perfected the form, he was THE master of Vaapad. It'd be a brutal fight, but in the end I favour Windu's chances over Anakin's. It'd be equally tough as Mace vs Dooku, but the victor would be the same.
Winner = Mace Windu
