Well, I'd say that there is an easy logical way to answer the question.
Let's assume that the most powerful being in Middle-earth was of
good nature. In that case the main force of evil (Sauron) should succumb to it. That would mean that there should have been no need for the Quest to destroy the Ring, since the most powerful being could beat Sauron in a direct confrontation.
But that didn't happen in the books, so i think we can assume that this isn't the case.
So let's assume that the most powerful being in Middle-earth was of
evil nature. In that case there are two possibilities: Either it is the main Antagonist Sauron, or a rival to him. If a rival to Sauron was in fact more powerful, then the forces of good would have most likely prioritized the fight against him or the rival would have openly attacked Sauron. Both again did not happen in the books.
That's why I'd say it's safe to assume that
Sauron must have been the most powerful entity in Middle-earth during the Third Age. Otherwise, why bother with the secret mission to destroy him without the use of open force/power?
Because there were beings in the elder days that could challenge Sauron openly, and we do have examples for confrontations like this: The Battle of the Last Alliance ended (not at all like in the movies) with a fight between Sauron and an all-star team of Middle-earths mightiest heroes: Gil-Galad & Elendil, probably with the help of Isildur, Elrond and Círdan. The first two even died, but all together still managed to
defeat Sauron.
But those days passed away and there are no such powers (for good) left in Middle-earth in the Third Age. I think this is mentioned, or at least implied at the Council of Elrond, which again is why they decide to destroy the Ring in secrecy.
Concerning Galadriel:
Well yes she definetly is very powerful, but again she never went out on her own to directly confront Sauron.
She didn't had any restrictions on her actions in Middle-earth like the Istari. In fact she left during the Exile of the Noldor, which basically banished her from Valinor.
It is said that Fëanors words
concerning Middle-earth kindled a desire in her heart, as she was eager to see those wide unguarded lands and rule a realm of her own. http://tolkiengateway.net/wiki/Galadriel So Galadriel went to Middle-earth with the desire to rule, and even renouncing the Undying Lands to do so.
I think its not farfetched to assume that Galadriel would have destroyed Sauron if she could do so without the One Ring, because
she tells us that this is exactly what she would do
with the One Ring. The Speech that she gives to Frodo (which was a bit overblown in the movies) reflects that Galadriel spent a lot of time thinking about what she would do with the One Ring, and describes how she would rule everyone as a unbearably adored queen. There is a lust for power in Galadriel (although in the end she rejects it/the Ring).
So yeah, Galadriel is actually kinda sketchy regarding her motives and her actions in the books (another example: Why is she testing the hearts of the fellowship members in Lórien, prodding into their darkest fears without consent?)
Therefor I think that she actually couldn't be stronger than Sauron, or else she would have challenged him.