They're only 'better graphics' in the sense that they allow some DX9 features if you still aren't on DX10, and they tend to emphasize the bigger more noticeable stuff than the smaller. It's really designed specifically for medium-settings DX9 rigs.
My rig has 8600GT. It's a DX10 card, true, but that's all it really was in it's own time. Beaten by any other up-to-date card back then, while only allowing DX10 features to be used. Though, it's still pretty impressive I guess. My CPU is AMD +5800 x2 2.8ghz, which I guess is the best feat of the rig. And 2 gigs of DDR2 memory.
So, I'll consider this as a medium-setting DX9 rig :]
EDIT: By the way, I consider my rig to be quite not so bad. I still have 2 DDR2 DIMM slots to fill, I can update my bios to actually turn AM2 socket into AM3 socket etc. It feels like biggest disturbance is my graphics card.
Should I just buy a new computer or rather a new graphics card and upgrade slowly my computer, until I need completely new one? I was thinking about getting 4 gigs of ram, look out for the 6000 series cards and possibly upgrading my 350W Macron PSU into a better one, for now. I feel like my processor is doing just fine, at least after each dustclean I make.