The answer is, of course, it depends.
Stainless is slightly less efficient than copper at heat transfer, but not grossly so.
Copper oxidizes over time, so you should keep a copper chiller clean of all green deposits. A slightly acidic bath of water and vinegar does the trick. Stainless should never corrode or oxidize (unless it's exposed to a highly caustic/reactive solution).
You sanitize and use both varieties in the same manner.