The first build has a better processor, better gpu. But i dont know about that power supply. If i were you i would check it out good before purchasing it. Other then that i would probably go with the first build.
Just wanted to add that the gpu on the second build is a 7870 XT, not the standard 7870.
And about the power supply on the first build, can you check it and inform me, as i am not so good into such stuff, but it said it had 38 amps on the 12 rails and 80+ bronze?
Core i5 3570k > get the ivybridge cpu, it's better than the sandybridge i5.
ASRock Z77 Extreme4 > good motherboard for the money, it's better than the asus LX.
Gigabyte 7950 or the 7870 tahiti le, the performance difference is minimal.
Noctua NH-U12P > if you can't fit in the budget, look for the cm hyper 212 evo or arctic cooling freezer 13 or i30.
XFX Core 550 > get this psu, it's a quality one.
Corsair Carbide 300R > good quality case, much better than the cm case
No, i asked two friends of mine to make builds for me for less than 850 euros, and they both came up with those two builds, each one tell me that his is good, so i can't decide, i am from slovenia by the way so the prices are a little bit higher.