Why do either?
Japanning is not an easy process I hear. Painting requires a lot of preparation work, only serves make to the plane a little prettier and could actually decrease the value of a collectible. I would suggest just a light coat of shellac on the surfaces normally japanned at the factory. It makes the plane shinier, helps prevent rust, and is easy to reverse without damage to the plane.
Having said that, it is your plane and you can paint it if you want to. It might bring a few more dollars at the flea market or on EBay if you don’t advertise the paint. True collectibles should only be restored by professionals and most of us repair and tune without true restoration.