I do agree with other posts in the sense that Obi-Wan was a master of form III, which was said to directly counter Anakin. I have an additional point though which I believe explains the way the movies play out.
I think what is lost here is that through the course of the fight, we see a parallel between the two fighting styles. The fact that the two use force push at the exact same time is evidence of this (although the freeze frame looks silly here):
You see many sequences where the two follow the same sequence of attacks if you watch closely. That explains the stalemate for much of the fight. The two knew each other so well that they could predict each others attacks.
Towards the conclusion of the fight, we see Anakin somewhat taunt Obi-Wan when he is ready to finish him:
Anakin Skywalker: [raises his lightsaber] This is the end for you... my former master.
And I think we see that when Obi-Wan escapes even after Anakin made his victory claim immediately angers and enrages him:
After this, Anakin goes on tilt and makes a mistake (ask any MOBA player what that is like) and the fight is lost.
In conclusion, I believe the movies show us that the duel between Anakin and Obi-Wan is nearly a complete stalemate. When Anakin could not break the defense of the Form III he becomes frustrated and fatigued (remember its really really hot on Mustafar) and he acts outside of his training and knowledge, leaving himself vulnerable and costing him the battle. This is the perfect reason why Form III is so strong on a Jedi and why the fight in the end goes to Obi-Wan.
Also, the goal of many Soresu practitioners was to prolong the fight,
the idea being to cause the enemy to become fatigued or frustrated as
they attempted to keep up their offense. However, this tactic ran
the risk of fatiguing the user if said user was to face an adversary
who could maintain an aggressive but cautious offense. - Wookieepedia on Form III