The award is for the BEST THEATER SCORE. Not the most "hummable" (whatever THAT means) or the one that makes you want to get up and dance or do another ten minutes on the treadmill.
For my money, the only two nominees that fall into this category are THE VISIT and FUN HOME because they are actual theater scores. They do what wickedfan says--
"...craft at all on the skill that went into a score. ...seamlessly it transitions in and out of its book ...shapes a character's arc or the beauty and intelligence of its lyrics or the dramatic structure of a song"
THE LAST SHIP, as pretty as some of the songs are, is a pleasantly bland collection of pop tunes. It's a nice song cycle in a funny sort of way. It's not a theater score. And SOMETHING ROTTEN is a series of self-referential, loud jokes and endlessly diatonic.
So if we're talking about the Best Score, I think it's FUN HOME, too. And I think the award will go to FUN HOME. There's a lot about THE VISIT I love, and I worship Kander and Ebb, but aside from the fact that it's Tesori's "time" in the eyes of some people (whatever that means, again), it's really dazzlingly crafted, full of surprise, and even...hummable. Not that THE VISIT isn't, but I wasn't as enamored with the Schoolmaster's song as some people.