Six of one, half dozen of the other Max. You'll find either of those cards, the nVidia or AMD will suit your purpose just fine. If there is anyplace to stretch your budget, at least IMO, it is your GPU. If you can afford to jump up to the 7950 from the 7850, the payoff is pretty good, particularly with that 3570k CPU overclocked. For about another 100$, you can jump up from the 7850 to the 7950, or for around half that much, approx 50$ more, you could move up to the 7870.
Just floating some ideas for you - I know a TON of people with the 7950 card, in fact, the 3570k/7950/etc/etc is a very "standard" gaming and do-it-all configuration. Skuzzy has that 7950 I believe, Mace, and several other BBS persona of note, maybe ask them if they think it's worth it if you're going to go AMD for your GPU. I have a squadmate with the 7870 and we has nothing but great things to say about it, and his CPU isn't as fast as your new one will be.
As for brands, it's pretty subjective, but I've read a lot of hate from the "hardware" sites like Toms etc regarding the HIS brand. Then again, I've read a couple of guys swear by their ICE HIS cards. PNY also has a sort of shaky rep from what I've read, many people accuse them of sourcing the absolute cheapest parts available, and have an equally bad rep warranty wise. Again, subjective, but very common to see BBS posts regarding the same opinion. Asus, MSI, Gigabyte/windforce, XFX, and Sapphire all have a fairly solid rep from what I've read as well, but again, it's subjective. One thing I've read pretty much universally regarding AMD cards is the XFX has by far and away the best and easiest to deal with warranty program. If you google "best AMD brand video cards", you'll get the phone book from Tomshardware etc, spend half an hour or so reading through some of the opinions there would be my advice before narrowing down some of the question you may want to ask some of the AH players here.
Other than that, I would ask Debrody, he reads and knows a lot about the AMD cards and their value/performance/quirks, or Chalenge as well. My vid cards are all nVidia now, but I ran an ASUS 5770 for a year or so back when it was "the" card, and it punched way above its weight for a long time. As I said, there are a lot of AH players who have all three of the AMD cards you should probably be considering. Sorry to blather on, but like I said, the GPU is the most important decision you have to make now that you've picked the CPU you have, and if you plan on keeping it as long as your last system, you should make it with the most and best info you can get IMO.