The Beach Club is one of our favorite resorts. With your kids' ages, they will LOVE Stormalong Bay and October is great weather for pool time. A short walk and you're in the World Showcase between France and England. Also can boat or walk to the Studios. Just cannot beat the location or the pool.
Last year, which was our third stay at the beach club, we did a split stay between the Beach Club and Animal Kingdom. While we adore the Beach Club, we fell in love with the peacfulness of the Animal Kingdom Lodge. But, I think part of why we fell in love with AKL is that our daughter is now 11. So we tour the parks very differently.
If it were my choice, taking into consideration the kids' ages, I'd go with the Beach Club.