Both.
Funny you bring this up, as I have been writing about why the East's par 3 4th hole is used in Royal Melbourne's Composite course instead of the East's fantastic 16th. Although the 4th looks and plays differently from other par 3s on the Composite, the 16th's unique beauty increases the aesthetic variety while not conceding the functional variety (the shot you must play). The 16th is not as long (boilerplate for pro-level "difficult") as the 4th, so it gets the axe -- even though it possesses some truly nasty hole locations.
Regardless:
Variety, absolutely. Variety is a good unto itself, for variety introduces new decisions and new shots. Variety is complexity in the sense of that word meaning many parts or pieces. Also, it contributes to memorability.
Difficulty could be the same hole in different places. This is the what I feel is the sole genuine weakness in Pinehurst #2; the par 3s are a little bit like two pairs of mirror images or reverse twins.
As to real world examples of variety:
Par 3s: Addington, Rye, Royal Melbourne West
Par 4s: Royal Melbourne Composite -- gap -- Ganton. Come to think of it, Lundie has a wonderful mix, too.
Par 5s: ???
Mark