Let's see:
FX-6300, $110 @ NE (w/ $10 off which ends tonight. Thus regular price $120. Still, arguably $10 cheaper)
i3-3220 for $119 on Amazon
And those two
head-to-head on AT Bench
With regards to gaming in particular, the AMD chips are fine to pair with a single GPU up to around the $250-$300 range, as evidenced by that one AT article where a bunch of CPUs were paired with the 7970 and everything ended up GPU limited at good looking settings with the resolutions most mainstream screens would be gaming at. So when planning out components for mainstream builds, there doesn't seem to be much reason not to take a good look at the AMD wares. One idea which seems to be often thrown around is that at some future point new games will take advantage of the Intel chips (e.g. person A says: "who cares if the i5 gets 195 FPS and the FX only gets 140" to which person B replies: "but a couple years from now, that could mean the difference between 60 FPS and 45..."), and I find it interesting to think that with the new consoles' influence, it might be the extra cores which end up gaining value first.
As you say, it would probably gain slightly -- and I'm not saying that it would be night and day either -- but it seems to me that the opposing SKUs under $200 are for the most part close enough as it stands now, that with a little lucky nudge from the console game programmers, AMD could find itself in a position like the one they were in when I bought my first chip from them years ago: Selling more bang-for-the-buck than the nearest priced Intel option.
Which I would find pretty cool: Going into 2014 with new next-gen console ports popping up and AMD maybe finally catching up and surpassing this good-ole 2500K with Steamroller or something else.