Annealed copper wire, that was annealed correctly, will be very soft and easy to apply, but will ''work harden'', it will get quite stiff and hold well for a number of years once it is in place. Biggest issue, if you don't get it right on the first pass, it hardens and becomes difficult to adjust placement of wire once you put in down the first time. Unwiring a branch and rewiring with the same wire can be very difficult, as the wire will be so stiff there will be the risk of breaking the branch. Once in place work hardened copper wire will hold the branch in position for years if necessary. Even the feral neighbor's cat rubbing against the tree won't necessarily knock the copper wired branch out of position. Once applied, the branch stays there. Critical for conifers where you wire them and then leave them wired up for 2 years or more.
Aluminum wire is ''infinitely'' flexible. Much easier to use especially with arthritic hands. Problem is, the aluminum wire needs to be close to the same diameter as the branch you are wiring in order to have ''holding power''. Second problem is if you move your trees around, or bump them while watering or have a neighbor's cat rub up against them, the aluminum will move, usually every month or two I have to remember where I originally put the branches and move them all back into place because they got knocked out of position.
So each has its strengths. Aluminum is cheaper, easier to work and rework. It is used most often for deciduous trees with wood that hardens quickly, like hornbeam, Azalea and others where you really only need the wire on for a couple months. Because it is cheaper, you just cut the wire off in little bits after it has done its job.
My arthritic hands will hurt at the end of a 4 hour wiring session with copper. I hurt a bit less with aluminum. I've learned to use both. The more I use copper the more I like the results. But if you want to avoid arthritic flare ups, aluminum is the way to go.