They actually perform about the same, so I would recommend the Athlon X4 750K for the sake of efficiency. That's assuming you plan to get a video card as well, ofc.
If you're not getting a video card, then the A8 5600K would be better.
Both are decent processors but it depends on what you plan on doing with it. If you want to use the A8's onboard graphics then I would get the apu. If you plan on installing another graphics card then I would get the athlon. If you plan on overclocking either of these I would strongly recommend an aftermarket cooler like the coolermaster hyper 212 evo. If you plan on using the apu's graphics alone then I would also recommend some nice and fast ram since integrated graphics use the system ram and benefit from the extra speed, graphics cards have their own ram so the extra speed would not be necessary.