We've eaten at both, and enjoyed both very much!!
Actually, Bomas is a family favorite, and a "must do" every trip!! The soups, the BBQ ribs, Zebra Domes - all are GREAT!!! There is a kids section - usually with mac n cheese, chicken tenders, french fries, etc. It is a buffet and the selection is absolutely wonderful!!!
DH and I ate at Jiko's for the first time this past Oct and we really enjoyed it!!! DD ordered off the kids menu - I'm pretty sure she got mac n cheese (but there was pizza and I think chicken tenders on the kids menu). DH and I enjoyed our meal (except for the obnoxious kid at the next table)! We would definitely go back. This restaurant is not a buffet, and is quieter than Bomas!
Both are really good; and definitely worth checking out!! Be sure to check out AKL gift shop too! Enjoy!!