Hi Jene,
If it is in your budget, then yes I would absolutely, highly recommend
Disney's Beach Club Resort over a Family Suite at
Disney's All-Star Music Resort, especially given the ages of your children. In fact, the Beach Club is one of my very favorite resorts. The pool, 'Stormalong Bay" incredible. It is nearly three acres with a sand bottom, whirling waters, a lazy river and a giant slide...all in one pool. Additionally, it is within walking distance of Epcot, a short boat ride to Hollywood Studios and across the lake from the BoardWalk area. The differences between a Deluxe Resort and a Value Resort are countless.
That all being said, the Family Suites at the All-Star Music Resort are quite nice. It is one of the only options to put 5 guests all into one room in a Value Resort. The pool doesn't have a slide or any of the other special features that the Beach Club has though. Additionally, your dining options are quite limited.
In a nutshell, if you can make it work with your budget, I believe you will love the Beach Club Resort and you'll be so happy that you chose to stay there.
Have a wonderful vacation,
Kaylene