As was already stated, it really depends on exactly when you're going. If it is during Spring Break, there will be alot of children. Other times not so much.
The Radiance-class ships, of which the Brilliance of the Seas is one, are really nice ships - our favorite within the RCCL fleet. However, while they do have a nice children's program, it is relatively small by comparison to other classes of ships that are alot more 'kid friendly', such as the Voyager-class, Freedom-class, or Oasis-class ships.
But again, this would also depend on the ages of the children. Younger kids will find the Brilliance to be fine, but tweens and teens would much prefer the other classes of ship to be a whole lot better for them. And of course as all parents know, if the kids are happy, the parents are happy!