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This is more complicated of an issue than most people here are making it out to be. Speaking generally of "The Maul that was," Palp would have won, however after a hard and strenuous fight. Mauls history as apprentice mentions a test Palp sent him through, at the end of the initial test Maul fought Palp in combat after days of surviving in the wilderness with droids chasing him constantly, which he failed miserably. After Palp pointed this out, he threatened to kill Maul for his weakness, at which point Maul attacked Palp, and they had it out in a fight that even tested Palp, after Maul was exhausted from days of surviving. It is possible that this Maul in peak fighting condition would have defeated Palp, however, this Maul was also far too loyal to even consider challenging his master, focusing all of his ambition on defeating the Jedi, instead of putting some aside for the want for Power.

But when we consider the "Maul that could have been," the possibilities change entirely. As I said, Maul was too loyal to challenge his master, if Palp had instilled the ache for power that was held by the master, Maul wouldn't have put all of his energy towards fighting the jedi, but also finding a way to defeat his master. If Maul had survived the fight with Qui-Gon and Obi-Wan, one he lost only because his ambition to defeat the Jedi overtook him, there should be little doubt that Palp would have trained him to a far greater extent, having truly proved himself. Various masteries of the Force would have become available to Maul, traits which he could use against his master. And at least in my mind, Mauls skills with a Lightsaber where lightyears beyond that of Palps; even if Palp did take out 3 jedi in a just a couple of moves, those jedi didn't really know what it was they were getting into when they went in that chamber.

This could be covered for paragraphs, but with this information, I think it's possible for people to see that the "Maul that was" was only incapable of defeating Palp because Palp himself trained Maul in a way that would ensure his own survival as mantel of the dark lord. And the "Maul that could have been" only never existed because Palp trained him solely as a sword, and not a fully blown Sith... anything.

Palpatine was afraid to lose his power because he knew Maul was capable of doing it if trained right, and so he then decided that to not complete Maul's training was the best course of action to complete the next 31 years he foresaw.

um hello? Darth Maul is Sidious' apprentice. Palpitine would never let him become stronger than he is. Remember Darth Plagus? He taught Sidious everything he knew, and then Sidious killed him in his sleep. Not to mention Darth Maul never used Force lightning. The only things Maul has is his double lightsaber and his youth.

Palpatine its just so obvious.