Not another war capable question! haha.
I would say if you just want to spend the least amount with no overclocking get the FX 6300 as it can cope quite well in all modern games (I have one overclocked and its still decent). Very good in multi threaded games/apps as Tehy said above.
i3 has stronger cores (even though it has physically 1 less than the 6300) and will provide on average a higher fps in most titles (mainly current and older single/dual core reliant games).
The thing about the i3 is that is has a nice upgrade path if you want to get your feet wet before splashing out on a beast such as an i5/i7. People are arguing that the AM3+ socket (FX series) is dead and AMD had no further plans for it.
Up to you really, I am not...