The difference is indeed RAID. RAID is 'Redundant Array of Inexpensive Disks', or 'Redundant Array of Independent Disks'.
The DQ6 supports RAID on the soutbridge (hence the R). RAID simply means that you can use multiple hard drives either to improve performance (RAID0), to increase data security (RAID1), or both (RAID5, RAID10, and RAID0+1). Two or more hard drives act together. In the case of RAID0, data is written to and read from two hard drives at the same time, which makes these processes a lot faster. In case of RAID1, all data on the first disk is copied to a second disk, so you always have an automatic back up. RAID10 and RAID0+1 are combinations of RAID0 and RAID1, and require at least four hard drives. RAID5 works differently to improve performance and data security, but I don't recommend it for a onboard controller since write performance will be pathetic (requires at least three disks).
The DS3 does NOT support RAID on the southbridge, but DOES have a secondary controller over the PCI bus which supports RAID0, RAID1, and JBOD with a limit of two disks (JBOD is 'Just a Bunch Of Disks'; two disks act as one larger drive, without performance increase).
If you really want advanced RAID, then the DQ6 is your choice. RAID over the southbridge is generally better than over the PCI bus.
HOWEVER! If you consider the DQ6, you should also look at the ASUS P5B Deluxe, which is the better overall motherboard.
If you just want excellent overclocking performance, and just run a single drive, or maybe a basic RAID, then the DS3 will do just fine.
PS: also look at the ASUS P5B-E, which is not too much more expensive than the DS3 and does boast the ICH8R southbridge.
Ok.. this post got a bit long.... I wonder if it would have been faster to look up a FAQ about RAID... LOL