Being cooler than all your friends isn't a hardware thing --well, not computer hardware at least.
However, as someone who has one of the monitors you have, and just did the upgrade myself, I'd say it depends. You'll get some benefit from the 2GB of video RAM when using multiple monitors. You'll get much better tessellation performance, though whether that's important depends on the games you're playing. You'll get to turn up antialiasing probably an additional notch from what you have it on right now for games. There may also be a slight increase in stability, but I think that's subjective.
There are some games where performance increases may be negligible for now, though I'm thinking ATI may unlock further performance with new drivers, since the 69xx series uses ATI's new VLIW4 instruction set, and drivers may not be fully optimized for it yet.
I did it partly because right now was when I'd get the most money for my 5870. I don't think I can completely justify it, but it is a nice card.
If you want to be the coolest, though, upgrade your GF --or be the only one of your buddies to have one.