Stainless is significantly more expensive and yet as
@Brewnaldo points out, copper has about 20x better thermal conductivity (413 versus 14.4 W/m K). This makes it work considerably better in a heat exchanger application regardless of scale.
So long as copper is properly looked after, ie. allowed to build up an oxide coating, it will not react with the hot wort (see
The Alloys of Brew). John Palmer has excellent advice on how to clean copper before the first and subsequent uses here:
Brewing Metallurgy - How to Brew which is worth reading. HOWEVER an important and often misunderstood point is that you should carefully avoid any direct electrical contact between copper and stainless elements in the presence of wort, as this will result in rapid electrochemical corrosion and ’off’ flavours. So
don’t let your copper immersion chiller rest on the base of your stainless brew kettle (but the odd brief contact while stirring would be OK). Equally don’t fit a brass tap or copper pipework to your stainless kettle unless you use insulating washers or a short section of silicone hose in between.
The most significant factor however is the one that
@DocAnna refers to, which is that a counterflow cooler (whether a tube-in-tube or plate design) is massively more effective than an immersion chiller and also a great DIY project; e.g. see
Build a Counterflow Wort Chiller - Brew Your Own