You didn't specify which model of Amd Athlon's processor you'd like to compare to i7.
Anyway, these days Intel is a step in front of Amd processor's, but their price is high.
To conclude, if you want the fastest processor, go with i7, if you want a fast processor which surelly achieve your demands and is cheaper, go with Amd.
I personally own an Amd Phenom II x4 b50 at 3.5Ghz and I'm satisfied by its performance.
Athlons are not, and never were close to the same category as any of the i7's. That's like asking - "What is very fast between a Ferrari and a Toyota Camry?" (not counted something that was modded up to the extreme). Yes, Athlons are cheaper than most of the i-series processors, but they are also slower than or only comparable to pretty much all of the current generation i-3, i-5, i-7's. My advice is to research (Wikipedia is a good start) the different Intel and AMD processor lines, rather than ask a question of which is faster, in this forum, because you will likely get some answers that oversimplify things like saying that Intel processors are the best on the high-end, AMD's are the best value. That may have been partially true at different points, it is not very true currently. Example - even the lowliest current generation i3, the i3-2100, is roughly the same price as the AMD Athlon II X4, yet benchmarks around the same or even a little higher. The AMD chip is true quad-core, the i3 dual with 4 threads thanks to hyperthreading - does this make a difference? Maybe.
Price differences are all relative - for instance, is ~$100-$120 the very limit you can spend, or would you spend another hundred on top of that to get a processor (i5-2500K) that is going to leave the Athlon II X4 in the dust? It's all up to you to find the price/performance point you are most comfortable with, but in any case, now you know that the i7 is waaayyy faster than the Athlon series, faster still than the AMD Phenom II and new FX series, but the gap is closer there in some applications. That is just considering the standard, unlocked i7-2600K processor, at around ~$330, sometimes less, sometimes more - and NOT the Extreme $1,000 Sandy Bridge that the other poster was talking about. Once again, you have to ask yourself - "Is spending $200 more for the i7-2600K over the fastest Athlon, worth getting a processor that is a lot faster?" Some would say, "yes", some would say, "no, because the Athlon will do everything that I will ever want it to do for the next several years".
+1 ^ Yes, this is the best and most concise answer. OP - you can probably ignore the other posts (including my previous post), since they all talk about price/performance, which you didn't even ask for.