Jambo is the original Animal Kingdom Lodge building with 1200+ rooms. The fifth and sixth floors were taken over by
DVC about 5 years ago and converted to villas.
Jambo is home to most of the noteworthy restaurants (Boma, Jiko, Mara) and most seem to agree that the lobby and other public areas are more impressive. However all of the rooms are 5th floor (except concierge on the 6th) so you're fairly high up. Also since the villas are converted hotel rooms many of them have their own idiosyncrasies (i.e. wardrobe instead of a clothes closet, no stand-alone shower.)
Kidani was all new construction and consists entirely of villas. IMO the lobby isn't as impressive as Jambo. It only has one restaurant--a table service location--which only serves lunch and dinner.
The rooms themselves are much nicer. Larger square footage than most older DVC resorts. The One and Two Bedroom villas have an extra bathroom.
Both have nice pools but Kidani is probably better suited for families with young children. Kidani has a good sized water play area with forts, water guns, etc. If you have kids 10 and under, they will probably like it. If older kids or no kids, the water play area isn't of much value to you.