The problem with trying to decide whether a musical from an earlier era is overrated is that we cannot view it through the eyes of its contemporaries -- as the Talmud says, we see farther than our ancestors because we are standing on their shoulders.
I happen to think that "My Fair Lady" is one of the greatest musicals of all times, and not overrated at all. In 1956, when it opened on Broadway, the changed ending would have been revolutionary -- an erstwhile misogynist falls for a woman because she exhibits spirit and independence, unlike so many other women of the era. As for why Eliza returns to Higgins: The musical hints that there is much that happened off-stage --"This ring isn't the jeweler's. It's the one you bought me in Brighton. I don't want it now." In other words, they went to the beach, he bought her a ring (a RING) and she's been wearing it until after he ignored her part in "his" triumph. The layers of the story, to me, make it timeless. I think Alan Jay Lerner managed to improve GBS's story by softening it and removing some of the misogyny. In 2013, that's impressive. In the 1950's, it was extraordinary.
As for the most overrated, I'd say "Oklahoma," with the Talmudic caveat in mind. The story makes light of the very serious dispute between the cowboys and farmers, and presents a heroine who is a shallow ninny. On the other hand, the choreography was considered revolutionary, especially with the use of the dance doubles. But, considering "Oklahoma's" numerous revivals, most people apparently disagree with me.
You alone can make my song take flight.