I prefer the lighter decor at the Beach Club, but a lot of people prefer the YC, especially the CL lounge, because it is a little larger. Plus all rooms at the YC have full balconies, but some rooms at the Beach Club, including club level, have smaller standing only Juliet balconies. Beach Club is a little closer to the Marketplace gift shop/snack/meal location, but if you are staying CL that would not be as important to your family
Both resorts have the same management, same food offered in the lounge, have equal access to the pool.
If you have the time, check out the first page of the Yacht & Beach FAQ thread. There is a lot of information and pictures of both resorts. There is a CL post, with pictures of the lounge and offerings and a post in the FAQ post (13?) that highlights the differences in the two resorts.
You can click on the link in my signature.
Dee