I saw both on Broadway.
"Cinderella" is accessible fare with pretty sets, a nice score (classic R&H so worth hearing, but also not at the level of the scores to "Carousel" or as catchy as "Sound of Music," IMHO), gorgeous costumes, a fairy godmother who belts while flying through the air, and a predictable romantic plot. I enjoyed it and the kids around me seemed to have a great time.
"The Color Purple" left me breathless and I returned two more times. [SPOILERS] It's a harrowing piece about a 14 year-old black girl who was impregnated twice by her own father then essentially sold into an abusive marriage, and how she claws her way out of the bad situation she's in over time and with the help of a female former drug addict with whom she falls in love. [END SPOILERS] It's a tough piece to watch compared to the family fare that "Cinderella" is, though entirely worth it if you are into drama. The score is stunning and I've listened to the cast album many times. I found it cathartic each time. As a previous poster noted, it has one simple set with minimalist props and costumes.
I haven't seen the tours of either, so I can't comment on the quality of the singing/performances, though I've heard great things about "The Color Purple" tour from friends who've seen it in my city.
If you think your family can handle the tough aspects of "The Color Purple," I'd say it's a no-brainer and go for that one. If you think your family would not respond well to a show that includes stark racial inequities, violence, sexual abuse, and a lesbian relationship, take them to see the safe, sweet "Cinderella."
Whatever you choose, I hope you all have a great time at the theater!