Kodak nowadays only has its Portra line of films in 220 (160 VC/NC ; 400 VC/NC ; 800)

According to Fuji's literature, all Fuji films available in 120 (including chromes; excluding Reala) are available in 220. But if you don't like chrome for your purpose, the options left are 160S, 160C, 400H, and 800Z.

In sum, your choices in colour 220 are the competing equivalents between Fuji and Kodak. I personally prefer Kodak films for reasons of colour palette (most people prefer either manufacturer for similar reasons).

I would say the only slight advantage in terms of offering on the Kodak side is that its 400 films come in saturated+contrasty (VC) and normal (NC) versions, whereas Fuji's only has one kind of 400.

There you go!