I've built and used a lot of different PCs both at home and at work as a test engineer.
I've found a big reason why S1 and S3 Standby (Sleep) mode behaves differently for different computers (i.e. people) is that the various motherboard manufacturers are NOT on the same page on how Standby (ACPI 1.0, 2.0, 2.1, etc) should be implemented on their hardware.
Moreover, different settings in the BIOS complicate matters when the BIOS OS setting is set to Plug and Play or NOT.
So when one person reports a method which fixes his Standby mode, it may NOT necessarily work for another person who most likely has a different motherboard in his computer.
In fact, I've read that S3 needs to setup in the BIOS BEFORE the operating system is even installed because Windows will install different HAL (Hardware Abstraction Layer) or ACPI files depending on the particular Power Saving settings in the BIOS.
AFTER the OS is installed on a computer, subsequently changing S1 to S3, or S3 to S1, may (or may not) change the Standby behavior on that computer.
Trial and error, and searching on the motherboard's website for newer versions of BIOS is the most practical way to research it.
When I go to the motherboard manufacturer's website for BIOS updates, I often see that a BIOS was updated because there may have been fixes for Standby, Sleep, or ACPI issues or behavior. That tells me they didn't know HOW it should been have implemented before they released their motherboards. And then consumers had to complain or send bugs reports to them before they try to fix it. And sometimes, they release several fixes before they get it right.
Generally, BIOS updates are NOT recommend unless you are having a serious issue on your computer because the REAL danger of screwing up a functional and working computer is introduced when performing a BIOS update.
"If it ain't broke, don't fix it", is the operating maxim when it comes to performing BIOS updates...unfortunately.
But if the Standby issues are really bugging you, and you're willing to "live dangerously" and risk bricking your motherboard while performing a BIOS update, go for it.
I've updated many a motherboard, and I usually makes me hold my breath during the actual BIOS updating process.