It depends on the program you are trying to run. Any game that is more gpu dependent, the core 2 duo with the 260x will probably perform better. That 220 will severely bottleneck that 6300, more so I'd say than the core 2 duo to the 260x, but neither situation is preferable. Can you wait on the upgrade and do both at once at a later time? Otherwise, you're not really getting a great upgrade in either direction.
If I had to recommend one though, I'd say the 6300 since you will get to a more modern platform that will be capable of upgrades the next few years vs the core 2 duo with the 260x since by the time you upgrade your platform, the money spent on the 260x now could buy a much better performing card that would better suit the whole new platform for the same money at a later date.