Number of cores is really irrelevant if 2 cores can beat 4 which in this case it does. Even in general computer usage 2 cores is all you need, the only place the x4 is better is video editing software or the like. The amd build will cost more since you have to buy a better heatsink to OC and a bit higher power consumption. You even have to OC the phenom and still have less performance than the intel. Don't get me wrong I'm not an intel fanboy, 2/3 of my last computers were amd but at this moment, intel has got amd beat in gaming price/performance at any worthwhile gaming rig.
But really either choice will game well at this somewhat low end price. Just make sure you get a am3+ board with that 965. I might even suggest a 955.