Well first off saying that the A10-7850k is a 12 core chip is bit misleading. It has a 4 core CPU and 8 GCN GPU cores.
With that out of the way, the specs look good.
A couple things to note:
1) prebuilt systems often skimp on the power supply (notice how it's not listed) so you may be replacing a dead PSU in the coming months
2) if you upgrade the discrete GPU beyond a Radeon 250 then you will lose Crossfire compatibility with the APU's GPU.
Personally, I'd go with the second system you posted, the AMD FX 8 core machine, and use some of the money you saved to upgrade the discrete graphics card from a Radeon 240 to a Radeon 270X (or whatever fits your budget) . Having four extra cores will help with modern games like Battlefield 4 and Crysis 3--games that are CPU bound and take advantage of all the cores you can throw at them