It is actually quite simple.
Before this 4870 I owned a 5770. My best friend was gaming with a GeForce 7900GT and I felt bad so I gave him my 5770. Shortly there after another good friend of mine blessed me with my present 4870. I am very familiar with the performance of the 5770 from actual first-hand experience. I know what it is capable of and its limits.
As such I'm also researching upgrade possibilities. I really want to enjoy Crysis 2 in all it's DX11 and High-Def texture goodness, as well as Skyrim and BF3 with all the bells and whistles, not to mention Prey 2 when it comes out next year.
That said, I would argue one of two things:
a.)Keep the card.
The 7 series are going to be launched mainstream parts first, higher end parts to follow. Seeing as how you first bought the 5770 and are now looking at the GTX560 I can safely assume you're concerned with only the mainstream parts and not the highend. As such, the mainstream of the 7 series should be available as early as next month, as late as the beginning of next year. It is likely that the "7770" will offer near 6970 levels of performance, at under $250, while consuming less power and producing less heat. Even if the wait is 2 months, far worth it in my opinion. This is likely what I'll be doing instead of buying anything right now.
b.)If you cannot wait-
hapooh is selling 3x 5870s for $90 each
. At $90 one of his 5870s is a considerably better deal than even the GTX560ti. Not to mention for $180 you could buy two of his 5870s and completely crush anything nVidia or even AMD offers in the $200 price range. Not sure if your mobo supports CrossFire or not so you might be just limited to one 5870. Honestly, if you cannot wait to upgrade your card then I'd recommend picking up one of hapooh's 5870s. Will nearly double your performance at a fraction of the price of a GTX560.
Regarding your processor- forget about Bulldozer. In most scenerios a PhenomII x6 will be faster. I'd buy the PhenomII x6 and shoot for 3.6 - 4.2Ghz. Plenty of CPU power for quite some time to come.
Maybe after a couple revisions Bulldozer will be competitive but as it stands, it's not worth the money and wouldn't really be an upgrade.
As to what you should upgrade first... I'd say upgrade your CPU, buy a PhenomII x6 first. Then as soon as the mainstream 7 series is available pickup one of those. If you cannot wait a month or two to upgrade your video card then pickup one of hapooh's 5870s (or two if your mobo supports CrossFire).