OK, here's what I've been doing with the SIII. I really like scrollable wallpaper. Coming from the Droid X, I'm just used to it. So I've been running
Apex Launcher and
WallPaper Switcher and use my list of
Droid X wallpapers. Some of the images are taken by me, and OBVIOUSLY some are not. I have WallPaper Switcher set to change every 45 minutes. That way, I never know what my wallpaper will be when I wake up my phone. And I've NEVER noticed a battery drain on my DX or SIII from this app. That's it. Works great!
And it never fails. If I decide to show someone something on my phone, it's ALWAYS Perry the Platypus as my wallpaper. Never a shuttle pic, never a moon pic, Perry! But I live with it cause I like Agent P.