They are both basically 'ballasted' couplers. The ballast length may vary from coupler to coupler and from company to company but the Kodak couplers always ended in a nonionic moiety, whereas the Agfa couplers ended in an ionic moiety.
During WWII there was free exchange between Agfa, Konica (then larger than Fuji) and Fuji which was a tiny company compared to the others. They all shared technology including color methodology. In the 60s, to foster efficient coating, all companies converted to the Kodak method or they just could not coat fast enough with few enough defects.
Kodak never sold a color product using the Agfa method, but the other companies now all use the Kodak method.
The ballast is there in all cases to prevent couplers from wandering. The bigger the ballast, the less the wander, but then the lower the ratio of 'dye' to 'inert' material in a coupler, so it is an art to balance off these forces in any design of coupler.
The ballast also affects dye hue. The 'resin' or 'coupler solvent' also affects the hue of the final dye. Oh, one additional thing. The resin protects the dye from oxygen and other agents that cause fade, and therefore improves dye stability. Early Agfa type prints using similar couplers to Kodacolor couplers faded much more rapidly and it was not until the other companies started using the resin or droplet dispersions that they were able to begin to catch up in that area. Now, of course, it is a see saw battle in dye stability between Fuji and Kodak.