We've stayed at both and greatly prefer Jambo. My son is now 8, and we've done 10 AKV trips. With a small kid I liked a quick service (even with my kitchen and grocery delivery, sometimes it's just easier to go buy a smuckers sandwich from the cooler than to go back to the room). He loves both pools now, but when he was smaller preferred Jambo. Kidani has a baby slide and a big slide, as well as a spray park area--he disliked the spray and was afraid of the big slide but felt too big for the baby slide. Jambo slide is perfect, you can see them at the top and the lifeguards have typically been lax about parents waiting to catch their kids as long as you aren't being a bother.
As for rooms, when he was small we got a two bedroom (grandparents came too) and we used the master bath for his packnplay (it's big). Kidani one bedroom has two baths, unlike Jambo's one bath for one bedroom. A packnplay fits in the extra bath of Kidani's one bedroom, if that's a thing for you.
As adults, we like Jambo b/c the lobby is impressive, the cooking smells are amazing, the bar feels special (Kidani bar is inside Sanaa...more like a waiting for a table bar, than having a drink bar).
As for animals, we've never not seen them and typically get a Standard one bedroom at Jambo, so the view isn't always guaranteed. I take my chances on this so that I can take more trips.