First of all - your 9600GT is a rebadge of the 8800GT, - so when looking at benchmarks, look for 8800GT if 9600GT isn't listed. You can check out Anandtech`s benchmarks over here:2011 GPU Comparisons2012 GPU Comparisons
As to ATI naming:
5000 series are cards from about 2 years ago. The 57xx are DX11 cards, first gen (best bang for buck as entry cards late '10, through early '11). The 58xx cards are faster still, and the 59xx are the fastest of that era.
This repeats with the 66xx is a rebadging of the 57xx line (much like your gt9600, mentioned above). The 67xx cards are third tier cards that came out more recently, the 68xx and 69xx cards are their fast and faster original lines (respectively).
The 7xxx series are even faster, and way out of your stated budget. Hell, the 69xx`s are far out.
As to the xx, they are incremental in their respective class. The ones you`ll be looking at are 50, 70, and 90, each being slightly (or significantly) better than the prior. there can also be a bit of overlap, where a 6870 might be as fast or faster than a 6950 in some categories, but not consistently so.
You can check out anandtech.com or tomshardware.com to get an idea as to performance.
If you go with Nvidia (once again, look for a 460 GTX for the sweet spot), you`ll also have some advantage with tessellation and PhysX (which is beautiful in games like Batman:AA).
5000 is 2010 series cards
6000 is 2011 series cards
7000 is 2012 series cards
600 is entry level
700 is budget gamer level
800 is enthusiast gamer
900 is for those with money to burn
50 is entry
70 is mid-to-high
90 is high-to-extreme