The intels are great chips and without a doubt more efficient than the current line of amd cpu's but I cannot suggest building a system on a dual core i3 for a few reasons.
1-Value, a dual core i3 costs the same as a 6 core FX while only offering a couple more FPS in games and slower performance in most everything else compared to the FX-6300
2-Software coding, more and more wares are being coded to utilize more threads on more cores, i3 will soon be obsolete when most major titles can utilize 4+ cores.
3-1155 socket, this socket will soon be retired and investing $120 into it with a dual core is wasted money. If you want to go intel spend the money on a quad and future proof yourself.
4-Overclocking, i3 cant overclock where as with a $30 cooler 4.5Ghz on an FX-6300 is a cake walk widening the gap between it's self and the i3 even more becoming more of a contender for intel's i5 line.
These are just a few points i feel people on a budget should consider before investing into a dual core platform.