13.9 is the WHQL and 13.10 is beta. This is your chose look at the release notes and if you are looking for a fix to an issue you are having choose that one. The 13.9 can out after 13.10 because it takes a while to get through certification process. I have used both version without issues, but I'm sticking with the WHQL version because of some other software testing I'm doing.
Some same if your current set is working then why change. Just read the release notes that's how to decide.
AMD A10-5800K, XFX 7850 Ultra OC Edition 975MHz, 16GB RAM, Win 8.1 Pro 64 bit, MSI 7778 motherboard, 500W PSU, HP P7-1235, CCC 13.12 WHQL