Welcome to the forum Sorourke.
I was too young to really remember Cape Cod and I definitely adore the lake. It has a lot to offer. It is a great home base for many things to do in NH too. Lots within an hours drive. There are amusement type places for youngsters as well as nature type places that a family would like.
Would you rent a camp/house or go the hotel route?
Are you flying or driving? If it is a long way, which place is closer?
Do you have a boat?
Do you like to do things like hiking or do you like to veg out? Though I don't think you can with those ages!
If you need some good links to things in New Hampshire, let me know. I have many favorite sites.
Good luck in your decision