Personally, I would go BLT. i think BLT has a more 'adult' feel to it. Also, the convenience of MK and the monorail are big selling points. With AK, you rely on the buses to get everywhere.
Depending on when you can book that stay, getting a standard BLT at anything less than nine or ten months is very difficult. AKV-KV standard, should be easier to get. Both have a second bathroom off the entry in the one bedroom villa. You might be able to get a lake view BLT at less than seven months out depending on when you want to book your stay. Three adults might enjoy just spending time at the resort at KV. I know we like it. Plus you could book the Wanyama Safari for one afternoon/evening you are there. Pricy but very nice.
I'd choose AKL. I haven't been in a BLT room, but really dislike the atmosphere of the public areas. Hallways feel like hospitals to me. Just my opinion, of course.
DH and I have always loved AKL - their atmosphere is perfect for us. We always spend time in the public areas (pools/lobbies/savannah overlooks/etc). Victoria Falls is a great lounge. We have stayed at AKL-J post-cruise, and really enjoyed it. Would love to do the same at Kidani.
For a short stay, BLT gives you better location.
I personally love AKL and feel much more "at home" there. If you're doing a resort stay (not going to parks every day), I would take AKL every time. I know people complain about having to take buses, but we have stayed there several times with our family and haven't had problems with transportation, even when we go to a couple of parks in a day.
Definitely depends on your game plan. Are you planning on spending a lot of time in the parks or not. If so I would say BLT if not AKL is one of the best resorts IMO. Have fun whichever you decide