I've eaten at both multiple times. We always had decent experiences at Fultons, but Jiko is so much better in my opinion. If you like fish, Jiko always has an amazing fish dish (used to be monkfish, now halibut I think) with a lemon beurre blanc and vegetables that is out of this world. DH loves their filet with mac and cheese, and their short ribs. They have great appetizers--the taste of Africa has three different hummus like dips with assorted pitas--their flatbreads are amazing, and their desserts are top notch. I recall really liking the chicken too--they brought it to the table in a tangine, which was pretty neat.
Plus, they have an excellent wine list, all South African. The decor is very nice, and we've always had stellar service.
Hope this helps!