Depending on where you live you might not have a choice. There are building codes in each state and in cooler climate states some require you to use copper pipes instead of PVC.
If given the choice I would always opt for the PVC. Copper pipe has to be soldered and that solder is 50% lead. Over time you'll get residue from that lead in your water. I know you said you drink only distilled water but I don't think I'd want to expose my body to any kind of seepage that might possibly come from the copper and most certainly not the lead.