Since the 240 is .2ghz slower than the 250, the 240 would probably perform very similar to the 6000. If your deciding which one you should get definitly go for the Athlon II. Its newer tech, 45nm, runs cooler, overclocks much higher, so on and so forth. But if your thinking about upgrading to a 240 from a 6000 I would advise against it, its just not much of an improvement.
^+1. Apt observations. As an upgrade, it is not worthwhile. If you're buying new, get the 240. If you're buying new another thing to consider is the mobo you'll be getting. The 240 should be on an AM3 mobo, which can take all kinds of future CPU upgrades. The x2 6000 may come on an AM2 mobo (AM2+ if you're lucky), which has no upgrade path.