EDIT: I noticed that this post has all my CPU knowledge in it, lol.
You're lucky. I have recent benchmark scores for both processors. I'll post them later.
The EE 840 isn't a bad processor at all. Infact, with HT, it can handle 4 threads at a time. But that won't help you very much with gamimg at all for 2 reasons. One: Its a Pentium 4-based processor. Inherently, Pentium 4s aern't as good as AMD Processors during 90% of tasks which include gaming. Two: Its a dual core processor. No game currently supports Dual Core processors. However, when games with Dual Core support come out you'll benefit. You still suffer from it being a Pentium 4 though.
As for the FX-57; Its your best bet in the world for a gaming processor. There is no Intel Processor that can match the FX-57 when they're both at stock speeds. Even if a processor could match it in normal tasks, AMD processors excel in gaming because of their shorter pipelines, so the FX-57 is hands-down the best processor for gaming right now.
AMD's Dual Core processors, the Athlon 64 X2s, are better than Intel's Dual Core processors even at tasks that single-core Intel processors are better than AMD processors at (Did I lose you? Basically there is no way the Dual Core Intels can outperform Dual Core AMDs). This is because the 2 cores in the X2s can talk to eachother much faster than the 2 Intel cores can. The difference is something like, the Intel cores have to communicate over 12 inches while the AMD cores are right next to eachother and have to communicate over maybe a millimeter or less. Ofcourse thats not the exact difference, but its a pretty good example. ALSO, the X2s aeren't as starved for memory bandwidth as the Pentium-Ds and EE840 are.
If you're building a future-proof computer, or a computer that will last a long long time, you should get a Athlon 64 4800+. It has 2, 2.4Ghz processors and it costs somewhere around $880. Since Dual Core games will most likely come out in the next couple of years, you'll want to have a Dual Core processor on hand.
So, all in a nutshell; Go for AMD for gaming and get either a FX-57 for today's games, or get an X2 4800+ for future games (it will also run present games magnificently, even with only one core being utilized. It'll be like a Athlon 64 4000+).
Sidenote: If you're good at overclocking, you don't need to buy those processors. You could buy a FX-55 ($800-something) and overclock it .2 Ghz and make it a FX-57. You could even buy a Athlon 64 3700+ ($260) and overclock it .6 Ghz (not too hard) and turn that into a FX-57. There will be no difference between the FX-57 @ 2.8Ghz and the 3700+ @ 2.8Ghz except that the FX-57 will have unlocked multipliers.
Same goes for Dual Cores; You could buy a slower X2 processor and overclock it to 4800+ speeds. Watch out for the L2 cache though, you want the 1MB L2 cache versions.
Thats only if you're good at overclocking though. If you're not, don't bother.