That's a tough call for me. We have stayed most frequently at CSR, and my kids love it more than AKL. I'm surprised by the posts from people who have found CSR not to be child friendly - my kids both love the pool, the slide, the playground, the wildlife, the hammocks, the coloring pages at the food court, etc. CSR shows movies at the pool at night, has a campfire with smores in the evening, has a pool opening ceremony for kids, and the CMs play games at the pool all day long. Both of my kids would pick CSR over AKL, although they love to see the animals and DD12 loves Boma.
We haven't stayed at Kidani - we stayed club level at Jambo. The positives - great cast members, amazing theming, wonderful restaurants, the animals, the Kidani pool, the savannah view balcony, the lounge. The negatives - the beds were uncomfortable, the bus service was the worst of any Disney resort we've stayed at, it was very dark (as in someone reading the paper in the club lounge with a flashlight
) and the room felt smaller than CSR because the furniture was so big. AKL rooms are a bit bigger (340 sq. feet vs. 314 sq. feet), but the entry hall and the large furniture made it feel smaller. I like the room setup better at CSR - there are sliding wooden doors that separate the vanity from the room, so I could get up, turn on lights, shower and dry my hair without waking anyone. The vanity in the AKL rooms was around a half wall from the beds, so the room brightened when you turned the vanity light on, so I couldn't get ready without the kids protesting.
If you are considering a 1 BR at Kidani, I'd go for that for the kitchen, washer and dryer and second bathroom. If you are considering a studio, I'd stay at CSR - a studio gives you one queen bed and a pullout. Studios have a microwave, but you can request a microwave at CSR for no charge. If you are considering a room at Jambo, it's a toss-up for me - I liked some things better at CSR and some better at AKL. If you are planning to spend a lot of time at the resort, AKL offers great activities for kids. If you plan to spend most of your time at the parks and come back for an afternoon swim break, I'd pick CSR.
Edited:
I found the thread I posted when we got back from AKL that compared the two resorts (at least for our family). It is specific to Jambo, so some of the observations might not apply to Kidani. Hope it helps!
http://www.disboards.com/showthread.php?t=2380960&highlight=csr+akl