During our split (Kidani and BLT) stay a few weeks ago, the only thing that was a drawback for us was not having CS at Kidani.
AKL and Mara is a short walk/bus ride away.
While BLT doesn't have CS inside, the resort has much less walking and when crossing the skybridge, there's always things to look at (MK, monorails, Bay Lake, marina, parasailers, etc).
Also, one additional benefit for three 14 year old girls. If they want to be at a different pool by themselves, the Contemporary pool is very close to BLT. We had a room that looked out to that area and really enjoyed being able to see all the activity out there.
Both are great and I'm sure your family will enjoy either one.
Good luck with you decision.