Bandstand was my third favorite of seven shows behind DEH and Sunday ITP when we visited last week. Loved the music and dancing ( and I typically don't care for dance musicals). Haven't seen sweat, so can't compare.
Personally, I'd recommend Bandstand. (I saw the Broadway production, so I can't tell you how it has changed from Papermill, though I heard it has a lot with Andy Blankenbuehler now at the helm). It has great music and choreography (no surprise there, with Andy B.!). One song in particular was the one that stayed in my mind after seeing 12 shows in 9 days, and I had that particular refrain from Bandstand in my head for a week-- in a good way -- despite the fact that the show was in the middle of that marathon of theater. Also, I loved that the choreography blended East Coast and West Coast swing styles when they were dancing. Plus, having interviewed many, MANY veterans from WWII and Vietnam for a documentary project, I thought they did a very admirable job of representing the different experiences soldiers had returning from the war, and struggles they faced.