Darth Vader and Darth Maul are two of the most menacing Sith characters in the Star Wars Universe. One a sheer weapon fueled by hatred, the other a fallen Jedi who succumbed to the dark side of the Force. While both characters are extremely skilled, Darth Vader would be the clear winner versus Darth Maul.
If the history of both characters is examined, they have many similarities. As Sith Lords, Darth Maul and Darth Vader shared a hatred for the Jedi and showed no mercy towards their captives or victims. Eager to follow the will of their master, Darth Sidious, they both executed orders without question. The two of them proved to be well trained in the Force and lightsaber combat, which meant certain defeat (or worse) for their opponents.
However, they also have many differences - differences that give Darth Vader the edge if a confrontation was to occur.
First, Darth Maul was a trained assassin. His only knowledge of the Jedi was that they were to be eradicated by any means necessary. Darth Vader WAS a former Jedi. As Anakin Skywalker, he was trained in the ways of the light side of the Force. Vader was a former General as well (having fought in the Clone Wars), so he also had the edge in strategy and cunning. Although he no longer embraced the Jedi philosophy, these factors had to give him an edge as a Sith. The many battles he fought before and after the Clone Wars made him battle tested for any number of opponents - including another Sith. Any mind games or "cloak and dagger" confrontations would surely put Lord Maul at a decided disadvantage.
Secondly, Darth Vader had endured many lightsaber battles against both Jedi and Sith. Darth Maul had not faced a large number of opponents that used both sides of the force. On many occasions, Vader (as Anakin) had faced these types of foes. He would be more prepared to face someone who was trained in Sith combat. As Anakin Skywalker, he had faced Master Yoda's former padawan Count Dooku on two occasions - ultimately defeating him. We cannot forget the frequent clashes with Count Dooku's trusted assassin Asajj Ventress, or his vicious assault on the Jedi temple where many Jedi were killed. Also, he went toe-to-toe with his own master Obi-Wan Kenobi, pushing his former master to the limit. In Episode IV, Vader (far more powerful with the dark side of the Force), finally gained revenge by defeating his former master (the very same Jedi master who destroyed Darth Maul himself).
Moreover, was it not Darth Vader (as Anakin) who was the chosen one? He was to bring balance to the Force and once he turned to Darth Vader, he did fulfill the prophecy. Although Maul was fueled by hatred, Vader's hatred and anger was the stronger of the two. Unlike Maul (whose moment of hesitation ultimately caused his defeat), Vader had very little patience and never hesitated to Force choke a military officer, threaten a Princess, torture someone, or nearly kill his own son.
Finally, if there is still any doubt that Vader is the stronger of the two - he destroyed the Emperor himself. Although he sacrificed himself to save Luke Skywalker, he still defeated the most powerful of the Sith. Vader's level of hated for the dark side was so strong, he would injure or sacrifice himself if necessary. These are traits I do not believe Darth Maul possessed. To prove this theory, read the comic book Star Wars Tales - Issue #9. A resurrected Darth Maul and Darth Vader had a fierce lightsaber duel. Maul started to gain the edge during the confrontation. With Vader on his knees, he stood behind Vader ready to destroy him. When Maul hesitated, he began to question Vader's level of hatred. He asked Vader what could he possibly hate more - Vader replied "myself." Vader then took his lightsaber, pierced it through his own armored body and Darth Maul's body with one strike - thus defeating Maul.
Now that is a Sith Lord!