They are both pretty much the same. However if you were going to go with an AMD (AM3+) based setup, you NEED a good motherboard with a strong VRM section. That little Gigabyte board common to both of your builds has a very weak VRM (I don't even think it has 4 phases for the CPU alone). For a good cheap decent board, get a Gigabyte GA-970A-D3,
http://www.newegg.ca/Product/Product.aspx?Item=N82E16813128521. Weaker VRMs don't bode well for OC, upgrades or even longevity and reliability. ESPECIALLY with the new AMD cpus (bulldozer and newer), because they are very current-heavy.
As far as CPU is concerned, if you shop around, you can get a Piledriver based FX6300 or FX6350 for nearly the same price as the FX6100 which is the slower, Bulldozer based version.
As for the GPU, I would lean towards the HD7870 version. Although if your budget is VERY VERY tight, you might go down to a HD7850 to make up for the money spent on the better motherboard and CPU.
Most AMD builds with budget components become CPU limited for newer games, so the Piledriver upgrade is a good idea, as well as the VRM issue on the motherboard.
Also, I find the NZXT cases really thin and flimsy, if you had another choice, I'd suggest Bitfenix (anything)?