I think 1776 deserved score. It was a damned history lesson that worked beautifully, and an awful lot of that had to do with the score. I have always loved the Hair score, but I would not have voted for it for two reasons: (1) Hair was essentially a revue and the authors didn't have the challenges associated with making the score work in a more traditional framework, which I think would have been very hard...1776 would have gotten major points from me on that; (2) there are an awful lot of songs that are not much more than did bits, entertaining but not substantial.
While Hair clearly has a number of songs that have become popular classics and 1776 has none that I can recall, the weaving into a story dimension scored points for me.
Interestingly, I saw the movie of BOTH within the last 6 weeks (they must have both been on TCM, although I can't remember where I saw Hair). While I thought there were still too many tidbits that could have been eliminated, I thought that Milos Forman and crew did a remarkable job of inserting a narrative around the formless show. A little was corny, but not a lot. I have always thought that the Hair movie, along with Fiddler on the Rook, was probably the best translation of a Broadway musical to film in the past 50 years. Once upon a time, I thought that Oliver belonged in that category, but I can't sit through Oliver any more.