Agree with the above posters about Jersey Boys. I think what a lot of bio musicals are missing is a strong structure or framework to tell the story in, which makes it feel less like a Wikipedia list of facts. The fact that Jersey Boys was about 4 different members of the band who often disagreed about events I think helped it, as we got to see what each perspective was like (and the seasons helped chart the general trajectory of the band too). Meanwhile, I thought Ain't Too Proud just had too many characters and the constant revolving door of band members made it hard to keep track of who to care about.
Rick Elice who co-wrote the book for Jersey Boys later went on to write The Cher Show which I thought was a decent effort, but seemed a little messy. Also, for me personally, whenever there's a jukebox about a female musician, one act inevitably seems to deal more with her marital/relationship struggles, and that act always ends up being far weaker to me, like act 1 in The Cher Show, act 2 in Beautiful, act 1 in Tina, etc. I get that it's an important part of their lives, but what I'm interested is more of their artistry and how they got to where they are that they're big enough to warrant a musical about them.
I thought MJ was actually one of the better attempts (if you discount the omission of any Michael Jackson controversy). It structured the show around a specific period of time and an interesting moment in his career, and the flashbacks seemed to make sense for creating a picture of who he was and how he got to be there. We got to see his artistry in action with how he ran rehearsals, as well as his foibles with his demands and spur of the moment ideas. The main part that didn't work for me was just the ending, where it seemed like it didn't know how to wrap up the show, but I thought the journey to get there was quite well done.
I didn't think A Beautiful Noise was that bad, just a little boring as a lot of people had mentioned. There were no real stakes to anything, and I wish more of the therapy conversation had come in sooner since there was no real context for why he was in therapy or what he was trying to work on until the end (maybe others who are familiar with Neil Diamond would've known, but I did not). I had really loved Bohemian Rhapsody (also felt like it had a stronger structure with its bookends), so I had a bit higher expectations for A Beautiful Noise, but I can't say it was terrible.