I figured it was time to make this, so here’s 

-the musical score is fantastic in all of them, even the weaker songs are still great to listen to. see here, here and here
-staging for the musicals gets continuously better with each one, and the third musical looks and sounds fantastic.
-Along with staging, the costume design is pretty spot on with the anime/manga.
-the plots follow certain manga plots while also keeping to their own stories
*the first musical involves a cursed flute that can capture ghosts, and the second two shinigami who just didn’t want to die alone.
-the third msuical makes Madame Red’s death more heartbreaking with a funeral duet ft her and Ciel.
-there are musical exclusive characters that are really interesting.
-Yuya Matushita is a total dork as Sebastian, and really gets into his role
-Ciel changes in every musical, and they chose younger kids for him which works really well.
-The cast is very talented and have great chemistry together
-every single cast member is a giant dork when they are together and it’s hilarious to watch
-Ciel and Sebastian get really cool duets together 
-Sebastian serenades the undertaker with a sexy love song
-Grell tries to seduce Sebastian with song
-William sings about the rules, and the entire shinigmai dispatch sings a freaking techno number
-the plots go from ridiculous to heartbreaking sad, and are just great to watch.

you can watch the first two subbed
HERE (first musical: That Butler, Friendship)
HERE (second musical(in parts): the Most Beautiful Death in the World)

the third musical, Lycoris That Blazes the Earth, isnt subbed, but you can find it HERE

there are also backstage snipets that arent subbed, but are super funny. 
first musical
second musical (in parts)
third musical

“Off to a great start with mdnaskin products with my partners Mr. Matushita and Mr. Nakajima. #wehavemanydreams #mdnaskin #mtg” -Madonna