We both have the same mobo: Gigabyte Z77X-UD3H
Also have same: PSU, Ram, CPU
Okay, that is strange if you have identical sets. & it is uncommon for graphics card to crash on idle or low usage.
I asked if your motherboard is Asus P8Z77 because I read in a lot of forum that this mother board + the 670 have lots of driver crash & has recovered problem & the solution is to change the PCIe setting in the bios from PCIe 3.0 to PCIe 2.0
While your motherboard is not Asus, it turns out to be a Z77 chipset to so maybe it is worth a try. It is not guaranteed of course because your brother's set have no problem but things vary from chips to chips so who knows?