i have not seen either Jersey Boys nor The Drwosy Cahperone, but this is just my judjement, based on clips, TV performances, etc.
I think just because the music in JB was not written for the show, this does not make it "unworthy" of the Best Musical award. Jersey Boys did something that not many other jukebox musicals have done, and that is to put the existing songs into a comprehendable and non-generic stroy. Jersey Boys used the songs of the Four Seasons to tell their story. It was one of the first recent jukebox musicals to actually have a good story.
Jersey Boys was also well-crafted, and well-performed. It did deserve its award.
I personally enjoyed Drowsy more, but I think both of these shows deserved the award.
As for the "Best Book and best Score, but not Best Musical" debate, obviously JB could not be nomianted for Best Score, and I think Drowsy won because their book, like Jersey's book, was well written, and it also allowed Bob Martin to get some credit for writing his role Man in Chair.
Just my two cents.
I am a firm believer in serendipity- all the random pieces coming together in one wonderful moment, when suddenly you see what their purpose was all along.