I use both, depending on multiple factors, but mostly copper.
To begin, as I'm sure you've already researched, copper holds shape better with only ~ half the diameter as aluminum. Also, I work for a lighting manufacturer, so scrap copper wire is readily available on the cheap, whereas aluminum wire has to be ordered.
Aluminum, to some degree, is forgiving, so a poor wiring job (especially when first starting bonsai) can be adjusted much quicker than if it's copper.
All wire digs in if you leave it too long. I like copper on my junipers and pines as they're slow(er) growers and don't thicken as quickly as a deciduous. I prefer aluminum, if I have it, on deciduous, because I'm going to be cutting it off within a season. The thicker wire doesn't bite into the growing branch as sharply as thinner wire, and therefore the scar is lessened if I haven't caught it in time.
For the most part, the type of wire isn't going to be so important, as it's just used to train your tree. Most trees with loads of wire aren't ready to show anyway, so whatever alloy and color works for you. However, it is acceptable to have wire on show trees, and copper is preferred, but anodized aluminum is gaining more acceptance.