For reference I have stayed in GVs in OKW, BLT and BWV. I have two kids , 6 and 8, but often travel in group of 10 to 14 (then we need a studio too). With 8 adults and 6 kids currently ranging from 9 down to 6 months.
Of the GVs I have stayed in, BLT is my favorite with younger kids, and my personal favorite simply for the wow factor of the room especially with a MK view. But that is totally personal preference and I know many people hate the contemporary decor of BLT. I like the very contemporary decor, the huge window and high ceilings in the main living area and the large layout. I'm not up on sq footage charts, but it definitely feels the biggest to me especially with kids wanting to spread out. BLT also has the Top of the World Lounge, which we love, but only bother to use when we are staying there, despite the fact we could use it other times since they've changed the policy. The walking path to MK is my favorite way to go, but the monorail is a close walk over the bridge getting you to MK or Epcot via TTC. The pool at BLT is nice, but kind of bland in my opinion, but my kids enjoy it.
BW would probably win out with older kids where the HS and Epcot rides are a big pull, as are more frequent late nights. Again here, the easy walks to both Epcot and HS are huge pluses for me. I hate the bus! The GV we stayed in at BW was all on one floor. I'm told there is a two floor version, but I'm not familiar with it. The one we stayed in had a large living area with two separate areas for seating. This was convenient when we had 11 people there are few years ago. There were 6 adults and 5 kids. When we were in the room getting ready in the am, or between activities in the late afternoon the kids could all play or watch TV and the adults could sit in the other area. It is a Boardwalk view so it can be loud at times, but the fireworks don't usually wake our little ones up. My kids love the clown pool here.
I just stayed in a GV at OKW over New Years, hadn't stayed at OKW in about 10 years. I forgot how quiet it is there, so it was nice over New Years. I'd vowed to never go back for New Years, we did it for 12 years and I just got sick of the crowds and the increasing degree of obnoxious drunken behavior. This year we went for a specific celebration and did New Years outside the parks. The only GV we could get was OKW and it worked well for the quiet trip we wanted this time. The pool had changed since my last visit, and my kids enjoyed it - in a cool rain no less! The rooms have a decent size living area, and a large kitchen and dining area. The bedrooms were all good size, but my bathroom in one of the queen bedrooms was tiny.
I've never stayed at AK. I would like to someday, but as you can probably guess from my bus aversion, the inability to walk to a park is a drawback for me. That said, everytime we go to AKL we say we need to stay there or AKVs sometime. I love the theming there. From the floor plans it looks like Kidani has a layout similar to BLT and Jambo is more like BW -- of the GVs I've stayed in.
Probably a lot more detail than you wanted

But as I got back less than a week ago I'm in withdrawal