I've done a couple of group trips, stayed onsite with a group of 15 at AS Sports and that worked out well in all honesty, did a group of 6 stayed offsite in a private villa and disliked it, really wouldn't do that again for a number of reasons and going in August group of 8 staying onsite again at AKL.
Offsite issues - having to get two cars, trying to navigate, everything taking way longer than it should have done, parking fees/having to get from park to car park, not just being able to 'pop to x park for the evening', no free dining (although obviously this doesn't always apply!), not being able to 'do your own thing' I felt we were tied together a bit more due to sharing cars and sometimes you just don't want that, plus things got a bit tense. Not my favourite trip! The plus points were having our own pool and going to more offsite restaurants but you can do that anyway.
Onsite - just soooo easy, transport all laid on, no problems getting to/from airport, find it easier for advanced planning/coordinating multiple people, safe location (we took 8 kids on the one trip but at the hotel they could walk around on their own and we weren't worried about their safety at 13-16 years of age), front desk/staff for any issues - when we had a problem in our villa we kept having to call for maintenance people then that usually involved a wait, better atmosphere I felt.
Obviously every family is different but after our one trip offsite I have vowed that we won't be doing that again for the forseeable. I just prefer onsite and genuinely it works better for us - I know a lot of people say better savings are to be had offsite but honestly I don't think our trip came out much cheaper (although splitting a villa more ways might!) and I just felt the saving wasn't worth our slight lack of enjoyment.