Anthony: Not a Intel/Nvidia Fanboy, please don't mistake that from me. I prefer Nvidia because AMD doesn't support above 60Hz, which my older eyes need a 120Hz displays to keep my virtual head from being Bambi in people's quick scopes LOL. AMD also has withdrawn from producing a solution comparable to Intel at this point. While they may include more 'lanes' (true cores), programs did not follow suite, so a optimized threading solution (Hyperthreading) to create the function of two cores inside one actual physical one performs better in all applications at present. That AMD can't or won't come up with a similar innovation (which would trounce Intel if it could be applied to all current selling FX line CPUs) it has, in the game space, made AMD irrelevant as only it single top end chip (FX-8xxx) can compete now in the i5-Haswell space, and still nothing touches i7.
This then is the basis for the hardware I would suggest normally, a FX-8 ot i5, but real performance i7, especially as Intel knocked the price right off on the newer Haswell to be at the best price point instead of being a 'hefty amount'. But this is the line I think you and I differ on. *I* will not spend $500-600 or so just to get medium or low graphics just to say 'yeah I played that game', at that price, (as I mentioned) it be better and more 'cost effective' besides hell lot better looking to invest in a console if your at that price range. The majority of the people posting these questions tend to be Jane/Joe NoideaConsumer whom also ONLY expect that 'youtube' video performance level which is normally a 1080p display, at least 50Fps, and usually on High to Ultra (so it looks like that 'video I saw on the Internet') which again the systems you offered won't cut it for BF4 (been there done that for both your AMD and i3 solutions) and all the threads and even Forbes Magazine WatchDogs article stating the issue appears to be the 'porting to PC' and as such there isn't the optimized video coding the consoles enjoy, which makes PC performance poor unless you have the highest level machines (i7, Nvidia 760 or AMD R9).
So given all this I framed my response a bit differently based on these 'facts' (want me to start tossing articles, benchmarks, etc. out there I can fill this thread again to prove the point I am not spewing stuff in forum, but using the information from multiple independent authoritative sources?). As I said, I won't game minimally so I can get "games that can be played smoothly at lowered settings." It just doesn't jive to spend that much money for so little gain.