There is no easy or simple answer
It really depends on the usage scenario
which games will be played more often?
for long term the FX6300 should be better but by the time the gains appear, may it already be obsoleted?
this gen of games should use more cores due to consoles but will those same tweaks be applied to PC?
is there a upgrade in the near future?
how much does electiricty cost? the i3 tends to use less power so if electricity is pricey, the i3 might be better
if the person is willing to OC to say 4.5ghz out of the box or even down the line, the FX6300 can offer more value
if the person might upgrade down the line or dosen't want to OC the i3 wins out
will they be doing any recording, streaming or video editing?
you can see from xbitlabs, that AMD does better with productivity loads generally
http://www.xbitlabs.com/articles/cpu/display/core-i3-4340-4330-4130_6.html#sect0
for average consumer load, I would suggest an APU over the i3 or FX6300 since you don't need a dGPU and AMD at $90 is hard to beat
Pentium's aren't really an option till even more budget constraints are applied as pure dual cores are out