My copper coil has never gone green on me (yet). It sometimes develops a greyish coat of who-knows-what all over it. When it does I drop it in a bucket of PBW for awhile and it comes out all shiny.
I like the copper because it transfers heat more efficiently than stainless. Probably not a big deal but I haven't found any reason to replace my old roll of copper.
From what I understand this is sort of a misnomer. Copper does conduct heat better but the stainless chillers are made of thinner material. So they do just as well as thier copper counterparts.
Mine was graying this time. When I wiped it down it was green on my paper towel.