In very simple words: S3 means „suspend to RAM“, i.e. only the RAM is provided with power in order to enable the RAM to keep the actual condition of the system while “sleeping”. By using this suspend mode you can save more energy compared to S1, but because all other components are switched off during the “sleep”, the system fans are stopping too, so there’s no active cooling provided for the RAM modules although they’re under voltage – this maybe explains why some problems can occur using this mode e. g. in small cases on hot summer days...
On the other hand, S1 is the most simple of all ACPI-states, because in this mode only a few functions are disabled and you can wake up the system by simply pressing any key. During the resting period, fans are going on to run so there’s no danger of overheating the system while sleeping.
On my DFI expert I only use the S1 state because I have recognized that there are some problems with USB devices when waking up the system out of the S3 state (my former Asus A8N SLI Premium didn’t show this problem). But besides of this fact I never have had any trouble by using the ACPI function.
A tight overview of the different ACPI-modes is given here: http://www.lifsoft.com/power/faq.htm