there's nothing like the 6300 not doing well in black ops 2. If your windows is updated then it'll have the few patches microsoft released for the AMD bulldozer architecture.
I believe you are also running CCC 13.1.
game loading times mostly depend on the speed of your HDD. more than any other component.
can you try lowering your resolution and game detail settings to the 5770/955 level and check if it is same as before.