Katsu very much comes from the Japanese heritage. You are more likely to find pork (just "Katsu") than chicken ("Tori Katsu"), often a layer of omlette (Katsu-don).
What does seem to be absolutely consistent is the whole vesta-packet-curryness of it.

I'd go deep-fried, but it is nowhere as near as delicate a result as tempura.

Oh, and try on breaded shrimp ("Ebi...") - heaven!