The Galaxy S III does have Wi-Fi Power Saving settings, it's just that they are located somewhere else.

If you go to the Wi-Fi menu, where the list of available Wi-Fi networks to chose from is shown, you'll see that on the bottom right there is an "Advanced" button. Inside this menu you will find the setting "Keep Wi-Fi on during sleep", where you can select between "Always", "Only when plugged in" or "Never".

I hope that helps.