As I understand it, it's the GPU that requires 6 + 8 pins - I wouldn't personally try connecting it to a 6 + 6 pin PSU. I'm no electrical engineer, but it doesn't appear that the PSU is designed to handle that powerful of a GPU.
I was reading a TechReport review of Skylake today and was surprised to be reminded just how close the Phenom X6 1100T is to the FX-8300 CPUs in performance. The 1090T would also be right up there. Bulldozer was a great disappointment, and the Phenoms could outperform it in some cases, but I'd forgotten how close they were even to Vishera.
I've also been considering upgrading my GPU; I have a 6870, which would be roughly equal to a 5850, though lesser than the pair you have in cases where CrossFire could be used. I agree that the R9 380 (and its predecessor, the 285) are great options; other than the Furies, they're also the most recent cards AMD has tech-wise. I've stayed so far (and returned the R9 290X I had) after determining that the actual visually noticeable difference wasn't that great for what I was playing, even if the frame rates were vastly different at max settings.
DX12/Vulkan is interesting, and AMD's DX12 performance in initial benchmarks is surprisingly strong. I wouldn't put it as a major factor in deciding what to buy myself at this point, since it's still so early going, but if you plan to keep the card for several years, it may prove a good investment in the end, particular since from what I've read AMD's advantage is due to the hardware architecture (wish I'd saved the link to the detailed explanation - might be able to dig it up again if requested).