I voted for the beach club. It really depends on the parks or park you visit.
The monorail is nice when traveling with a stroller, also the boats are just as nice when traveling with a stroller, the pool at Beach club is the most spectacular pool in my opinion, for your children ages 12 thru 8. It truly has the wow facor and is well supervised with many life guards. The Beach club also has two parks close by that don't require a bus,EPCOT is so easy to walk to, 5 to 10 minutes at the most, and the back entrance to get in to the park is never crowded. The eye candy at night with the board walk and activities for the kids is magical and many free street entertainers along with carnival games to play. My kids dont want to stay anywhere else. They have movies on the beach with roasting marshmallows every night. My thing is that you never get bored there and yet it's very serene and relaxing at the same time: best of both worlds. Hope whatever choice you make works for your family as the Beach Club works for ours. Have a magical trip!