I love Jumby Bay, but would never describe the beach as amazing or comparable to those listed in the OP's post. In fact, the last time we were there, seasonal sea grass kept us out of the beach for our entire stay, but I understand that this is not a common occurrence. The service is superb and I imagine you would be very comfortable here with young children. For us, we were aware of the air traffic, but not in a way that was a deal breaker.

Before I would consider Viceroy Anguilla, I'd suggest looking at a recent thread on TA that summarizes the pros and cons: pay particular attention to the service comments and presence of a crane and noisy construction right off the beach.