Kidani is great...we've stayed at Jambo, but not at Kidani, but we've spent a fair amount of time over at Kidani...Their restaurant, Sanaa, is among our very favorites in all of WDW. The pool, kids splash area, and exercise complex are terrific.
Kidani is the first (of two) bus stops at AKV for buses that go to the parks (it's second for buses that go to Downtown Disney). It's quite close to the villas...Kidani is "sprawling"--probably runs 1/3 of a mile or so from end to end, but the bus stop is sort of "in the middle" (altho a bit closer to the side that's closest to Jambo)...so no matter where your villa is, you won't be far from the bus stop. We've never experienced any bus problems at all at AKL...buses come pretty quickly, both to the parks and from them.
Kidani has a pretty small gift shop in the lobby, with a refillable mug station and a small assortment of snacks & foods that can be prepared in the villa...it's about a 10-minute stroll over to Jambo, where Mara, the quick-serve eatery is.
Guests at Kidani have full access to amenities at Jambo (and visa versa), so your kids can go back and forth between the two if they want to experience the different pools, animal viewing activities, Community Halls, etc.
The villas themselves I can't give you any personal comments on, because we've only stayed at Jambo...but they do have an extra bathroom at Kidani which a lot of people really value.
AKL is very different from OKW ... the villas aren't as big and the decor is a bit darker...but I'd say the buses are better, if for no other reason than that there are five internal bus stops at OKW and only two at Kidani...
OKW beats Kidani, tho, in terms of "walkability"...OKW has so many options for just going for a walk (something I love to do, altho I know a lot of people think they get more than enough walking in the parks and in going to/from the various resort amenities)...I always feel just a tiny bit "trapped" at AKL...the only "real walk" is between Jambo & Kidani (and that's no more than 1/2 mile) and there's no safe, easy, pleasant way to walk outside the resort...at OKW you can take pretty (and long) walks within the resort, or head down the canal path to Downtown Disney and/or SSR...and both Downtown Disney and SSR offer interesting and pleasant walking opportunities, too...that's not an option at Kidani or Jambo.
Good luck in choosing. Both resorts are wonderful...I know I find whichever resort I choose, I love it and miss the ones I didn't choose!