I've never had a motherboard with such feature. And I've been building systems since 2002. What was that previous motherboard of yours?
This is part of the Award Modular Bios, that is used by GIGABYTE. My Mobo is a AM3 socket
MA790xt-ud4p. Also had this feature with previous mobos from Gigabyte.
2-7 Power Management Setup Page 50
AC Back Function
Determines the state of the system after the return of power from an AC power loss.
Soft-Off The system stays off upon the return of the AC power. (Default)Full-On The system is turned on upon the return of the AC power.
Memory The system returns to its last known awake state upon the return of the AC
I think I have seen this in the UEFI version on one of the latest GIGABYTE boards but cannot swear to it.
It is quite a handy feature where you have a remote server and you loose AC for a few minutes. Saves a drive to remote post.