And, after ten hours of much needed sleep (Faunus's mom can wear me out, lemme tell ya!), I am back to discuss the Galactic Emperor.
Force potency:
The Emperor has been identified as "the grim culmination of Sith philosophy and teachings", "the one born with the power to embrace the dark side fully and become its dedicated instrument", and the individual whom the Sith Order had been waiting for: one born with the power to return them from hiding to dominate the galaxy; the revenge of the Sith.
There can be no question that the Emperor's potency in the Force was vast; Luke Skywalker, in the New Rebellion, mentioned that the dark side threat (Kueller) embodied a sense of power that he hadn't felt since the Emperor, and mused that none of his students approached such a level of potency -- which implies that the Emperor's raw strength exceeds that of Kyp Durron himself. Moreover, the omniscient narrator of Revenge of the Sith identifies Palpatine with the dark side of the Force itself, referring to him as "the shadow" who was blunting Jedi sensitivity throughout the galaxy and casting the Force into darkness. In that same novel, Count Dooku would gaze upon Palpatine "through the eyes of the Force itself" and notice that Palpatine was simply "beyond power." In the Essential Guide to the Force, Mara Jade Skywalker recalls her time as an Emperor's Hand and notes that her powers were fueled by the Emperor's "vast reserves of Force energy"; this coming from a woman who had befriended and would later marry the powerful personage of Luke Skywalker. Skywalker himself, before his confrontation with Supreme Overlord Shimrra, noted that the Emperor was a "shell of a human in a cloak, more energy than flesh." According to Wizards of the Coast's article on Byss, Palpatine transformed the once-nascent planet into "one of the most powerful dark side sites in the entire galaxy" during his reign as Emperor; a time when he was primarily secluded on Coruscant. He would later use the Force to break the wills of its twenty billion inhabitants and leech off of their vitality to lengthen his own life. Dark Empire and the New Essential Chronology refer to the Emperor as a "dark side nexus."
Force mastery:
Statements from the Dark Empire Sourcebook and the Dark Side Sourcebook display Palpatine's knowledge of the Force to be particularly amazing. He has studied the Force in all of its guises, possesses a "wealth of Sith knowledge" even before his ascent to Galactic Emperor. He would later collect the greatest teachings of the Force from a million worlds and surpass any knowledge of the Krath and other esoteric Sith cults, including the Prophets of the Dark Side and the Sorcerers of Tund. The Dark Empire Sourcebook explicitly states that the Emperor's knowledge was so great that it was believed that he had mastered almost all of the known Force techniques, previously unknown ones, and that he devises new ones at his leisure. There can be no question that the Emperor's knowledge of the Force (particularly the dark side, even though he is also stated to be a master of Jedi knowledge as well) is unequalled by any individual throughout the whole of canon.
Lightsaber combat:
Emperor Palpatine trained Darth Maul in the lightsaber form Juyo, which was only to be mastered by "high end masters of multiple forms" which corroborates Nick Gillard's comments regarding Darth Sidious's mastery of the lightsaber. Palpatine's musings in The Essential Guide to the Force reveal that he was also a master of Teras Kasi, and was the one who indoctrinated Maul in martial arts. He was capable of imbuing himself with such speed to kill three celebrated swordsmen in under thirty seconds, compete with Yoda, and force Mace Windu on the defensive. He also has demonstrated enough skill to outline Darth Maul's figure so closely with a lightsaber that "the merest twitch of a muscle" would have dismembered the Sith apprentice. He also summons Darth Maul's lightsaber to him telekinetically in Darth Maul: Saboteur, ignites the blade, and performs psychokinetic feats with it, leaving Maul in "unabashed awe", suggesting that he may be capable of telekinetically wielding a lightsaber with great precision. It is evident that he found lightsaber combat to be the least of his Sithly concerns, mentioning to Vader that he only uses it to "humilate the Jedi." So while his actual skill in terms of swordsmanship may be surpassed by a handful of other Sith and Jedi, he is still an undisputed great with a blade.
Conclusion:
The Emperor's raw potency is undeniably vast. While he is not at the level of Anakin or Luke Skywalker, that is not to say that he does not rival other members of the Skywalker clan in terms of potential; he might even surpass most of them. His mastery of the Force is unequalled throughout the whole of canon by any singular individual. That is not to say that he is the most proficient in each and every one of its techniques -- as Faunus has mentioned, while Count Dooku's power will never approach that of the Emperor's, it is highly probable that the Count's mastery of telekinesis is more efficient and masterful than the Emperor's own -- but it means that he is at least master level with the majority of them. The fact that the likes of Darth Vader and the Emperor are still used as measuring sticks for power even by Legacy of the Force suggests that he has a parity with Luke Skywalker in most regards. If one were to compare the two, I would say that the Emperor's mastery of the Force is still greater, but Skywalker is the more capable combatant.
Lastly, that is not to say that the Emperor is without peer. Even throughout his reign, Palpatine kept a cunning eye on those who possessed the ability to challenge or defeat him: Inquisitor Jerec and the Nightsister Gethzerion come to mind. Luke Skywalker, Yoda, and Mace Windu as well. One would also speculate that Marka Ragnos, as well, could challenge the Emperor.