Go for the i5, it's a full 4 core part and will take your system to far higher level. The i3 is good, don't get me wrong, but it's still only dual core and Hyperthreading can only do so much when faced with a game that wants 4 or more physical cores.
If the motherboard supports overclocking, go for a 'K' series chip, otherwise stick with a non 'K' version, BUT...Prices vary wildly for these 'old' parts so if you can pick up a 'K' cheap, even if the MB supports limited overclocking you can run the rig stock for a while then kick in the OC later to extend its life.
There's not a huge difference between the i5 3670K and my own i5 4690K and, trust me, that is a monster of a CPU.
And either i5 will be far superior to the AMD FX6300 and in many cases the FX83XX.