The Rule of Two dictates that when the Apprentice surpasses the Master in power, becoming the greater of the two Lords of the Sith, the Master has served his purpose. The Apprentice must challenge the Master in open combat, fighting to their utmost, as the final trial: killing the Master and taking his place is the final proof that the Apprentice is indeed more powerful.
This is how Darth Bane, founder of the Rule of Two, defines power when determining how to ensure each master is more powerful than the last.
Darth Sidious, however, violated the requirements of the Rule of Two: By killing his master, Darth Plagueis, in his sleep, he did not go through the trial of a duel to the death to prove he has indeed become the more powerful of the two.
As such, there is a need to search elsewhere for clues to the answer. Is Darth Sidious more powerful than Darth Plagueis, according to Darth Bane's definition of power being battle superiority?
Canon sources preferred.