The Radeon card is far superior in Stream Processors. 1600 (800 x 2) Stream Processing Units. The GeForce card only has 240 processing cores. What advantages does more stream processors give? What are they used for?
The Radeon card also has a better core clock speed, 650 vs the GeForces 648. What differences does this make and what is it used for?
As for memory, both cards are sporting 512bit GDDR3 memory. The GeForce only has 1GB as oposed to the Radeons 2GB. The Memory Clock speed however is superior on the GeForce with 2484MHz(effective) to the Radeons 1986MHz. What makes what card better and why?
What tasks do each card perform better than others? I want to know what makes what card better, and why.
You have to look what kind of games you want to play with your pc/card. A lot of games 'favor' either nvidia or ati. Just use the reviews and benchmarks to make a choice what you want and look for reviews of that card to see if it is what it says
then there is the value for money story, we don't know what kind of budget you have, although youre looking for a high end card looking at your first post.
It is hard to compare videocards purely on the specs, they are just build entirely different. I hope you have a more clear view of the matter.