I don't remember if Jyggalag being said to be the most powerful, just that the other Daedric Princes hated him. I'm inclined to think their hatred was because of his overwhelming Anuic (Orderly) embodiment.
I've got strong inklings some Princes are more powerful than others, but I'd probably list my lord, Hermaeus Mora with Boethiah, Azura, Mephala, Mehrunes Dagon, Molag Bal, Sheogorath/Jyggalag, and Nocturnal.
Mankar Cameron is, well, an idiot. Given third hand knowledge he commented on to form a bogus religion. Lorkhan is the big daddy of Mundus, but he's an Aedra. I love that idea of Mundus being his realm though.
Sheogorath's power from Sithis is third hand as well. He was created by Lorkhan's death (his name is taken from Lorkhan. Shor (Nord) -> Sheor (Breton) -> SHEORgorath). His dual nature with Jyggalag is perplexing, but compelling even without his alter-ego's connection to Lorkhan and Sithis.
I don't even think Meridia is worth mentioning, to be honest. She's a Magna Ge who went Padomaic and created her own realm. I'd count her among the eight lesser princes to the eight greater I listed. If you disagree, I beg you to come after me. I'm aching for a good lore discussion.
But, you insult my Lord, and for that you must be punished. His power is knowledge, and his knowledge is vast and beyond his brethren. He is the Prince of Fate and Memory, and Knowledge. He is the Daedric equivalent to Akatosh in his influence and spheres, rumors of being created by Magnus himself as the scrapped blueprints of Mundus. He sees all, hears all, knows all.
I was going to mention that Alduin would be a candidate worthy of consideration based on some of the arguments found here, buuut...I don't think Alduin can even be considered...I mean, as the first born of Akatosh and all... D:
There are seventeen Daedric Princes (here is a list of them). Out of all of these I would have to say Jyggalag, as he was powerful enough to scare the other Daedra into forming an uneasy alliance so that he could be contained.
Really interesting discussion here about whether Hermaeus Mora is actually a fragment of Auri-El, that I think you'd enjoy reading (if you haven't already seen!)
I have, but thank you for the link. I disagree, but the connections between the two are why I listed him as one of the most powerful Daedric Princes. His continuous involvement in major events through agents is suspicious, to me, especially since they all involve Akatosh.