We have been toButlins lots over the yeas and Centre Parcs once.
Butlins is undeniably cheaper, especially if you buy 'activity vouchers' before you go. this means it is about £5 a pop for archery, high ropes, bowling,fencing, rifels,cinema, crazy golf, the boating activities etc. The fair is free, the discos and shows are free (although sometimes you have to get there early for a seat!). The waterpark is amazing (easily as good as centreparcs) and the dining plan is really good for food (loads of choice) . we have mainly been to skegness which has access to a most beautiful beach if you get fed up of the activities. there are also tennis courts and bikes to hire. If you do go consider taking kids scooters or rollerblades so they can zip around everywhere. We normally stay in the gold appartments - we stayed in budget once, they were clean (and close to the centre) but rather tired and a lot of people sat on their doorsteps smoking (unlike in the gold appartments apparantly).My kids adore it - I like the activities but i never know who the singers are. The pantomime is always a laugh though.Also if you are offended by other people having tattoos you will be offended a lot!
At centre parcs it was a lot more expensive to book activities (ABOUT 4 TIMES THE PRICE),but they were fun (crossbows, orienteering and crazy golf), and we didn't go to any 'entertainment'. There were a lot of trees and the squirrels were tame enough to be fed. Nobody smoked and everyone was middle class. The 'supplies shop' was extorionate. I did not eat in a restaurant. Lodge was nice.
So in summary: If you don't want to mix with the working class, don't mind paying through the nose for activities and want to cycle around through lots of trees, pick centre parcs.
If money is an issue, you have children that would spend all day in the water or running around given half a chance, children who love to watch singing and dancing acts and you actually don't mind that some people will be there with tattoos and some smoking (i say this because my friends husband loved the holiday at butlins but felt it 'wasn't his type of person' more fool him I thought - these people clearly love their kids as much as i do) then go to Butlins and book the money you have saved on a dining plan.