IIRC copper is very effective, but may cause some kind of internal organ damage which may impact fish's long term health long after ick is just a memory.
I may be wrong, but I beleive that I've read that somewhere.
Personally I've used both treatments at different times and found both to be %100 effective, but there are a lot of potential variables (different strains of the parasite with different tolerences, refractometer calibration issues, frequency of testing SG or copper concentration, target levels when testing both for SG or copper levels....)
After about 11 yrs of saltwater keeping, I have reccently learned the best kept secret of fishkeeping - QT everything, and treat all fish visable Ick or no visable Ick
Current protocol for me - all fish get acclimated to QT tank, then transitioned to 1.008 max SG for 6 weeks, then transitioned back to normal SG and observed for 2 weeks. All corals get a 6-8 week QT period to be sure any pests/predetors show up, and to allow enough fallow time for any ICK to die off.
It's a bit of a PITA, but I now keep a 40B system with sump, Skimmer, heater, good circ and a 150W HQI light. I have a garama and a damsel that live in the QT when nothing is being treated or QT'd, when I get a new fish or coral the garama and damsel go into my fuge and the new livestock goes into the QT. That may sound like a lot of effort, but it's way better than constantly dealing with Ick, flatworms, nudi's exct.....