Depends on what kind of vacation experience you're going for.
(Actually, it all depends on availability. We've been BLT owners since they first sold, but just finally got in this past month. We loved it, btw.)
AKV is great for getting away from the crowds and bustle and business of the parks. I love the savannah rooms--sitting on the balcony with a nice S. African wine, watching the animals wander around--pretty near perfection. But, getting around is kind of a pain unless you have your own car. If you're looking for a laid back, mellow kind of WDW experience, I'd choose AKV.
Like I said, we finally stayed in a 2 BR theme park view at BLT last month. I fell in love immediately. Lots of space in the room. Loved the design. Being so close to MK, having the monorail right there (easy transfer to Epcot at TTC) was wonderful. Watching the fireworks (the perspective is so different from TOWL!) was breathtaking. We often walked back and forth to the MK. Bus service to HS, AK and DTD seemed slow.
We've not stayed at BCV, though we have stayed at Beach Club. The proximity to Epcot can't be beat, but sharing bus service with so many other resorts is a huge pain. If you plan to spend a lot of time at Epcot (or even HS, a walk or boat ride away), this is a good choice. But Disney really needs to rethink all the resorts they cover with the Epcot area buses.
My suggestion? If you're staying long enough, do a split stay. My goal is to try every WDW resort some day!