BOOK OF MORMON tops any list like this for me. Hated the show, hated the improv-ish score and lyrics, hated the sense that this was a show built for kids who thought Broadway musicals are stupid.
FUN HOME-- I could appreciate and admire this show, but I was miles away from loving it. (Apologies to Dramamama who sat next to me at that early performance who clearly loves the show.) Went a second time to see what I missed-- still admired the cast but the show and score didn't create the spell for me they have for so many others. I much prefer Tesori's gorgeous score for SHREK, which I listen to all the time.
GENTLEMEN'S GUIDE TO LOVE AND MURDER-- charming but nothing more. Witty score and lyrics, much that's delightful in Act I, then a big nothing in Act II. A lost opportunity.
KINKY BOOTS-- Amateur score and worse lyrics, hated the barely-there take on British midlands folk, hated the predictable finale filled with LOVE ME, LOVE ME moments.
ONCE-- some beautiful music-making throughout, but I was really put off by the disconnect between the songs which were NOT expressing the thoughts of the characters much of the time. Eventually the disconnect made me tune out completely.
So basically I've had lousy luck at the Tony's for Best Musical for awhile. (In those same years, I'd have picked AN AMERICAN IN PARIS, BRIDGES OF MADISON COUNTY, MATILDA, ONCE (grudgingly) and THE SCOTTSBORO BOYS. Shows what I know.)