I've never seen Hamilton live, but I'm familiar with the soundtrack and the staging through "totally not a bootleg I got online."
Having now seen the official filmed version, I give it a pretty solid 7 1/2 out of 10.
SPOILERS!
Lin-Manuel Miranda is a genius at his craft. He creates fantastic songs and weaves tapestries of rhyme most people coudn't begin to even attempt. The staging and choreography are first rate. The cast is amazing and everyone inhabits their characters perfectly.
That said, I agree that the plot kind of meanders in the second act and never quite solidifies into a single narrative thread. Personally I think part of the reason for this is that Miranda pulls a switcheroo: after having 95% of the show be the story of Alexander Hamilton AS TOLD BY Aaron Burr (much the same way the story of Mozart is told by Salieri in Amadeus), in the very last scene Miranda switches and makes it all about Eliza. Eliza is great and she was obviously important to Hamilton's legacy, but I wonder if the show wouldn't have been stronger if they'd ended it with Burr's realization that "the world was wide enough for both Hamilton and me." Eliza, while a great person, had up until the very end been a supporting character; pushing her to the front just seemed awkward to me.
Some people have said the dancers are more of a distraction than anything else and the musical didn't need them. I can certainly see that argument as there were several times when I found the dancers weren't needed to get the point of the number across ("The Room Where it Happened" and "Wait for It", for example.) They were used to great effect in many places, but I'm not sure they worked in every single scene.
Also...the spit. Ugh. Anyone who's seen the film knows what I'm talking about. It was gross, unnecessary and should have been reshot. Points taken off for the spit.
Hamilton is creative, energetic, and a lot of fun. Is it the best musical I've ever seen? No. It's sometimes a little too clever for its own good and I'm not sure how well it's going to age. Somehow I can't see teenagers in 20 years rapping "Guns and Ships" in their high school auditoriums. Or if they do, it's going to have the same quaint feel that teenagers singing hippie songs in Godspell has today. A product of its time to be sure, but timeless? We'll see.