Using copper vs. stainless in your brewing system usually comes down to personal preference.
Copper is a much better heat transfer material and will provide the optimal chilling speed.  The thermal conductivity of copper is 20 times greater than stainless steel.  Copper also provides a yeast nutrient for healthy yeast production during fermentation and is naturally antimicrobial.
Stainless has become quite popular lately.  Stainless is more rigid and durable and will stay shiny longer.  Also, if you happen to be a low dissolved oxygen brewer (LODO), you will want copper out of your brewing system.
In terms of maintenance, we believe both our copper and stainless steel chillers are simple to maintain and clean.  For both copper and stainless, regular maintenance includes rinsing off the coils with water directly after each use (best practice is saving the first 5 gallons of chilling output in a bucket to dip your chiller in for rinsing), emptying the chiller of any excess water, drying with a soft towel and storing in a dry area.