If it is strictly for gaming and school work (which I assume is mild word processing music and such) it really doesn't matter and I would go with the cheaper option if money actually an issue. But if you want to splurge a little bit then I'd go with the Intel.
Well the AMD CPU is by no means bad, but if you can spend more for the Intel I'd do it, it is significantly faster especially in games. They both overclock well, so the FX-6300 isn't really gaining any advantage there.
I'm looking at some anandtech.com benchmarks and it looks like the 2500K is significantly better for gaming. We're talking at least 20FPS difference in Dragon Age, Dawn of War II, World of Warcraft, and Starcraft 2.
Well the thing you have to take into account with those benchmarks is that those numbers are based upon a build with GTX680 ($500 graphics card) where the CPU is much more likely to bottleneck the system, but in a build with using a GTX 660ti, the difference is going to be much less noticable as the GPU is more likely going to be your bottleneck than your CPU will be.
If you were to go with the AMD build, I'd suggest this mobo as it super good with OC (8+2 phase count and heatsinked mosfets) and has plenty of features. You should be able to get a 4.6-4.8GHz OC on the FX6300 with this mobo and that cooler.
Why not take some of the money you'd save from the FX6300 and drop it on a better GPU?
Lastly, avoid that PSU, you should go for this XFX PSU instead.
I would go with the AMD, in the past I've found that AMD last better for longer and not over priced like Intel but I would go with what CloudScorpion said with changing mobo and that. And it saves you more money. I know from past builds I have done for people that people with AMD computers have had less trouble with their computer then Intel clients have
I've found anything below the i5 price point (~$200) AMD's new chips take the prize when OC overhead is taken into account. The i3 market has been swallowed up by the A10/FX4300/FX6300, and will likely stay that way until Intel releases their new chips in however many months, where I'd expect performance to swing back into their favor. For gaming the highest I recommend on AMD's side is the FX 6300, after that the next chips to consider are the i5 2500k/3570k.