A[n] [surprisingly] insightful question, HWKA. I think we're all coming to realize that the "top dogs," so to speak are not completely untouchable or peerless in a combat scenario.
Board Walker
Scenario 1: Both are in a battle Colosseum and must fight to the death, they may use all their powers and abilities, they are equipped with their saber/s.
The reborn Emperor seems to have been somewhat out-of-practice when it comes to strict lightsaber combat. Though he is a master of Juyo, and thus a high end master of multiple forms, canon shows us that prior to the events of Dark Empire, he hadn't lifted his lightsaber against an opponent since his battle with Yoda in the Rotunda. Given the timeline for the Emperor's life, the man likely hadn't been using his lightsaber on something of an active basis since he trained Maul. The result is that he's obviously still quite lethally competent with a lightsaber, but that's a far cry from Skywalker's constant use of the weapon in life-or-death scenarios for decades. Skywalker clearly has the more practical experience and skill, if not the same level of classical training; Skywalker has a notable edge in lightsaber combat.
Not to mention the fact that Skywalker is a master of the shatterpoint charism, which would probably bring back unpleasant memories of Mace Windu.
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Board Walker
Scenario 2: A battle of purely the force, no sabers
The Emperor possesses a mastery of the Force that is truly unparalleled. As a Sith, he possesses the advantage in terms of a far greater arsenal of offensive Force techniques and the willingness to use them without hesitation. He has the advantage here.
Board Walker
Scenario 3: Melee combat, each may amp their own bodies and minds with the force, but must fight with hand to hand.
Skywalker seems, at the very least, decently competent in melee combat, but the Emperor personally trained Maul in various martial arts. The Emperor has the advantage here.
Board Walker
Scenario 4: Ship to ship combat, they have the same ship, but whose battle meditation and strategy will prevail in this tactical battle
Unless Sidious has a Destroyer, Luke obliterates him.