I don't want to start a big fight, it's not worth it, but copper wire does have some advantages over aluminum, especially on sappy, springy material like pines. It is definantly stronger wire. Same diameter wire, copper is considerably stronger. Annealing it will make it soft enough to handle easily to wrap the wire, but once bent, the copper metalic structure "crystalizes" into place. Which means that the more you bend it, the stiffer it becomes. Therefore, wrapped around a branch, then bent into place, the wire is stiffer, and will hold its position. Aluminum just doesn't do that. So, to get it to stay, you have to use a thicker aluminum wire than copper wire to do the same job.
You can use copper wire when doing guy wire training. Aluminum wire will stretch, and the branch won't stay "down".
Annealed copper turns dark brown when wired on the tree and left outside. It almost blends in with the tree. Well wired, it's unobtrusive.
Most aluminum is colored but still looks "fresh". And since the wire will have to be larger to be effective, it's more apparant when you look at the tree.
Copper does have it's disadvantages:
It is more expensive. If you wire a branch, and don't like it, and want to rewire, you generally can't unwrap and use the wire over. It gets set, so you'd have to cut it off. Aluminum you could probably unwrap and use again. Because it 'sets', it's more likely to cut in to the branch sooner than aluminum. Also, because you use thinner copper, the thin wire cuts in faster than aluminum. Also, to remove copper, you pretty much have to cut it into little chunks to get it off. Aluminum can be unwrapped.
I tend to use copper on my pines. Aluminum on my azaleas and zelkova. I use aluminum for tying trees in pots. I will use copper on my azalea and zelkova if the aluminum isn't doing the job of holding.