I'm 29 and I loved Beautiful without ever having listened to Carol King music before (I knew some of the songs but didn't have a CD or anything. Also, this is about the early stages of her career, so many of the songs in the show are written by Carol but performed by other artists, so there is quite a bit of variety.
I also loved Waitress. I cannot get the music out of my head - I'm currently pretty obsessed. But I also thought the Tony Awards performance was perfection, so I'm a little concerned that you didn't love it. She Used To Be Mine is one of the best songs of the show - however it might just be that you didn't know the context of the song. I'd seen the show before the Tonys, and so I knew the place where it was coming from emotionally in the show.
My vote would be for Waitress over Beautiful, especially since you can easily see Beautiful on tour now that all the original cast has left anyway. Seeing Jessie in Waitress is worth the price of admission alone. At the end of the day both are good choices though.
Never saw BoM, only listened to the OBC and it wasn't my kinda humor, so I can't advice on that.