OK, I just built a box (meant to be a fairly low/mid range PC) with an Intel i5-3750K. This has the built-in Intel HD 4000 graphics. I looked at the Passmark video card benchmarks and it's right up there in the mid-range cards, being out-performed by the $50 GeForce 9600 GSO! *facepalm* Seriously? The $33 GeForce GT 320 seems to have about 20% better performance?? That's really sucky. It would seem to make sense to spend an extra $100 and put some kind of graphics card in this thing, right?
I've now been reading and it seems the AMD A-series integrated GPUs are much better than the Intel ones. So I guess I should have build this with an AMD CPU?
You must be refering to games that you can play.
1) outside of gaming - games that rely primarilly on the GPU, the HD400 is fine - ie Playing a DVD/Bluray movie.
2) Some games are depenent on the CPU, while most are GPU dependent and while the on board GPU in the AMD build would have been better than the iGPU (HD4000) neither is considered a good choice for gaming.
Overall if you are going with a low budget gaming build with integrated graphics only then AMD APU's have better graphics, however as for the processor itself the i5-3570k is much better, it even beats a fx8350 in most cases gaming wise. If you can I would recommend that you get a dedicated GPU. If you can get a decent dedicated graphics card then you would have a powerful system as the 3570k is an excellent piece of silicon.
If you want to play games, you'll want a discrete graphics card whether you bought an Intel CPU or an AMD APU. The only exception is if you are limited by budget or case size to not be able to get a graphics card at all; in that case get the APU. Otherwise, once you add a discrete graphics card, any advantage the APU may have had goes away.
A GDDR5 version of the HD6670 will outperform the graphics portion of an APU.
In any case the 3570k itself is a fine CPU. However if you are playing games or similar, then it makes a lot of sense to buy a discrete GPU in addition. If you do not need a lot of graphical horsepower, then HD 4000 should do fine.