I suggest you disregard most of what jrgong posted.
With the new trinity chips out, it would make more sense to use those for crossfire with the 6670. The crossfire should deliver slightly less performance than a 7770 but should be significantly cheaper.
I would suggest the phenom II x4 or a 5800k and a 7770 personally. I am not a fan of hyper threading in exchange for real cores. A large part of this will depend on what game you play tho.
The 7770 would be somewhat better than an A10 with any 6670, but despite the higher price, the power consumption difference would also be considerable. I'd recommend getting the 7770, but like esrever said, jrgong is not very accurate about the reasons for that.
The trinity is really only good without a graphics card (price performance)
If you are going to buy a graphicsc ard, intel all the way.
That's very debatable. If you buy anything up to a 6670, then AMD still wins. If you go beyond that, then it's just a bunch of trade-offs without a clear winner except for very specific situations and different such situations can have different clear winners.
I'd still say the i3/965BE, if you have the option always get the single GPU setup.
Honestly, I'd go for the A10 over a Phenom II. I'm quite sure that it beats Phenom II x4s in CPU performance overall and it is far more energy efficient and I'm willing to bet that if you manage to disable the IGP, the A10s can overclock ridiculously well. I like A10 plus 7770 for this where the A10's Radeon 7660D is disabled. Even if OP doesn't overclock, it's still very energy efficient and has excellent value. Those A10s are priced well even if used as only CPUs
so choose the AMD because its slightly cheaper even though it runs much hotter, unupgradable ( AM3+ = dead ) and must be highly overclocked to even come close to matching the i3 in terms of performance ( and it still gets beat in everything that doesnt utilize more than 2 cores [ie most applications and all games])??... if he doesnt need the discrete graphics card then i would definitely recommend the AMD cheap as its IGP is much better than Intels token effort. However the i3 and 7770 is a nasty bang for buck combination. Ideally some more information is required before a "best" choice can be ascertained, however if your building from scratch and the price difference ( 20 bucks lol ) doesn't bother go get the i3/7770 hands down. .. and disregard the fanboy's advice (like esrever above me) and try to find truly objective literature based on what YOUR needs are ( can be difficult here i know)
Phenom II x4 is more or less on-par with i3s (wins some, loses some, but generally very close) in performance, so that theory of yours is busted. An A10 such as the 5800K is undoubtedly better than a Phenom II x4 in both performance and is far superior in power efficiency, so the Phenom II x4's higher power consumption is kinda irrelevant in this case.
Most applications do use more than two cores and the same is true for most games that are CPU-bottle-necked. Games that don't are mostly not very CPU-heavy games (there are very few examples otherwise, but I'll admit that there are a few such as SC2, but even then, AMD's quads do almost as well as the i3s in that game). Your view on software is a little outdated.
the i3 >>> phenom ii x4, however as you mentioned the 5800k is a much more viable option, but as other have said if youre going to get a discrete card then grab the intel chip all day
i dont think my view is dated im just being realistic on how much you'll utilize those extra cores on a day to day basis whilst the advantages the intel chip provide are evident every time you turn your machine on
Passmark is beyond inaccurate (it's a synthetic and is thus only good for comparing nearly identical models) and the Tom's article clearly shows how the Phenom II x4s are right with the i3s. That chart doesn't take BF3 MP nor some new games into account (the i3 wouldn't have a chance in those), so it's also a little inaccurate, but even without that, they're pretty darned close on average. Also, most modern software outside of gaming is able to use four or more threads quite well. So, yes, your view is dated.
The 5800K, as a CPU, is faster than the Phenom II x4s (also, an 810 has a very low frequency and less cache than the 9xx models, so it's irrelevant even if Passmark was accurate) as a result of its similar performance per Hz to Phenom II and its high frequency. It'd be in the same bracket as the i3s.
either way i think we both agree the a10 is a solid option, however the i3 is still faster in programs that use 1 or 2 cores ( which regardless of where were headed, this encompasses most every day computing and most games)