VS0G is a firmware provided by LiteOn, and VY08 is provided by Sony.
Patching the firmware with OmniPatcher will simply allow the firmware to operate on your drive. The drive is part of a generation of LiteOn drives, in this case the 2nd generation 2s series. Usually, only the firmware meant for the drive you have will work; however, with the patch, it will allow the drive to use any firmwares from within the same generation and series. The firmware will otherwise be exactly the same. It will still be VY08 or VS0G, whichever you choose to use.
VY08 will possibly cause the hard drive (IDE) LED to blink/light up at the same time as the light on the drive itself. There is an option in OmniPatcher to disable this feature. VS0G will NOT cause the IDE indicator to light up.
VY08 will also cause the drive LED to blink while burning, whereas VS0G will cause the LED to steadily light red while burning (with periods of orange light when buffer underruns occur, the drive is seeing if it can begin to go faster or if it should stay at the same speed, etc.). There is an option in OmniPatcher to make VY08 light the LED red while burning (as opposed to blinking green), should you want it to do so.
VY08 is slightly older than VS0G, but with only 2 less media codes in it. For most users, this will not be noticeable as long as you use mainstream media. Each firmware has its strong points and weak points. It is up to you to decide which is better for you.
Edit: VY08 is intended for the DRU-710A from Sony, so the drive will be id'd as such. The VS0G firmware was intended for the SOHW-832S by LiteOn, and will be id'd as such. OmniPatcher will allow you to change the names (drive ID strings) in the firmware. There is a list of all known drives within OmniPatcher, and it automatically presents you with names; all you have to do is select a new drive name, save the firmware, and flash it. This procedure also goes for setting any other patches to firmware with OmniPatcher. You may make as many changes to the firmware at once as you like; you do not have to change one aspect, save the firmware, reopen that one, change another aspect, etc. So you may set the drive name at the same time as you apply other patches you wish to use.