I think Princess is an excellent choice for a family cruise. There is a broad demographic onboard. I'm 38 and never feel uncomfortably young, yet I see passengers in their 20s and 80s. Average probably late 40s or 50s. Definitely fairly upscale, but never stuffy or overly formal. Yes, the formal nights are observed, but you have options and flexibility which works well for families. Good kids program, including some on port day. No in-cabin babysitting, but there is group babysitting available in the kids center many nights.
The other two mainstream lines which could be argued as more upscale, Celebrity and HAL, are definitely more formal. HAL's Zuiderdam works well for families, but not sure i'd give a blanket recommendation for the entire line. Celebrity can work for families as well, but is less flexible in dining, for example, for families. Definitely more formal in service.
