Actually, it is AK's official view that yes, body material DOES affect the sound. Since we use the entire body as a ground, Stainless Steel and Copper are more conductive than aluminum, therefore provide a better ground.
I've heard a significant difference between the AK380 aluminum vs the AK380 SS and Cu. Personally, I hear a lot less difference between SS and Cu, but that I just me.
Spending a few weeks with the SP1000M, there is a notable difference, at least for me. Again, sound is very subjective, so what I hear may sound totally different to someone else. I would highly recommend listening for yourself with your daily headphones/IEMs to see what sounds best for you.