Did Obi-Wan defeat Darth Maul with his raw skill and because he was better?

It was because he had the low ground...

He out-Forced him.

It was a conflict of dichotomies and ironies, actually. Obi-Wan, as with most Jedi, was not trained to fight other Jedi with light-sabers. Maul was specifically trained to fight Jedi with lightsabers. He was arguably thus more proficient at using a saber, and certainly a lot more viscous. He also clearly had solid Force training, though I remember hearing that when he Force Pushed Obi-Wan, he was actually drawing on the Darkside energy that Obi was unintentially drawing on himself, as he was filled with pain and rage over his master's death. He was doing what no Jedi is supposed to do: seek revenge. Obi was fighting Maul with anger, maybe even hate, and Maul turned that against him, and blasted him into the pit.

Up until that point in the battle, I think that Maul was a bit overwhelmed by Obi, because Obi was himself suddenly being vicious, fueled by rage. Hence why Obi managed to slice Maul's saber in half, reducing him to one blade. But AFTER Maul blasted him into the pit, IMO the real reason he lost, was hubris. He took his eye off the ball. Already having killed a MASTER Jedi, and now having a Padawan near-helpless, at his mercy, he clearly could not have even concieved of Obi-Wan Force Jumping out of the pit, over him, and slicing him in two. Which is why Obi is able to do it. And why Maul looks so genuinely shocked, because he clearly thought he already had the battle won, mission accomplished.

Maul was a great warrior, well trained in killing and battle. But he whereas he stayed hyper-focused on Qui-Gon, the REAL threat (hence him pacing and never once taking his eyes off of him), he also very much seemed to disregard Obi-Wan as not nearly as much of a threat. It was that arrogance that cost him, what should have been his life.

He outsmarted him. Obi Wan was at his peak fitness in this movie, but Maul was just better. Obi Wan had to fight smart to win. That's kinda his thing. He's more crafty than dominant.