Do you have a budget, or will you buy whichever meets your needs the best? What will you be using the computer for? The 5850 is a farily powerful card, what is prompting you to buy a new one? Would you want to overclock the new card? What are the specs of the rest of your system?
Sorry for the barrage of questions, but they're all important if you want the most accurate recommendation.
Not really a budget, but I've narrowed it down to those three cards. It's specifically for gaming, and the 5850 has started to just lag during massive on-screen graphics associated with MMOs, currently SWTOR Specifically. Plus I need to order a video card for a tertiary system I am building, so it presents an opportunity to upgrade this video card while moving the 5850 to that system to save money overall.
The rest of the system is Currently waiting to get and install an OCZ Vertex 3 as well)
GIGABYTE GA-890FXA-UD5 AM3 AMD 890FX SATA 6Gb/s USB 3.0 ATX AMD Motherboard
AMD Phenom II X4 965 Black Edition Deneb 3.4GHz Socket AM3 125W Quad-Core Processor HDZ965FBGMBOX
2 x OCZ AMD Black Edition 4GB (2 x 2GB) 240-Pin DDR3 SDRAM DDR3 1600 (PC3 12800) Desktop Memory
CORSAIR Enthusiast Series CMPSU-850TX 850W ATX12V v2.2 / EPS12V v2.91 SLI Certified CrossFire
COOLER MASTER HAF 932 Advanced RC-932-KKN5-GP Steel ATX Full Tower Computer Case
Get the 6970 if it costs the same as GTX 570. It will allow smooth gameplay at 1080P with everything maxed out including adaptive AA. Now if you can get the GTX 570 for $30-$40 cheaper then get that because it can do 60fps at 1080p with everything maxed out too. I've seen the galaxy GTX 570 for $269 sometimes on newegg. You might even be fine with a 6950 2gb...it will do 60fps too and can be bought for $230 sometimes.
for my personal use I went from a 5850 to a 6950 2gig card and have zero problems to date. A 6970 would be a little better. not knowing your res ( mine 1920x1200 ) I find that above 1600 res and using high/highest settings 2gig is needed.
guess I should say more than 1gig before people jump on that but wouldn't buy a card now that has less that 2gigs.
From personal use I find my 2GB 6950 handles everything I can throw at it. They are also very good cards to overclock. 6970 Will obviously perform better, but is more expensive.
If you are looking for a great value, I would buy the 6950 and overclock it. You can get some pretty serious performance gains through tweaking. otherwise, I would go for the 6970. It will perform better than the 570 at the same price point.
580 is too expensive for the performance it offers, if you are going to spend $500+ i would get the 7970 which easily outperforms the 580, and costs about 10% more.
Coming from someone who also plays SWTOR and has been reading the support forums quite a bit, just a slight caution... one of those cards (and I would pick the Radeon 7970) is going to help, but the game is so new that it's got a lot of optimization ahead of it. Many people with high-end cards still have performance issues.
If you want to go with something that's going to work semi-well with SWTOR now, then do the 580. But if you want longevity and are willing to wait for AMD to update their drivers, then do the 7970.
So you bought a GIGABYTE GA-890FXA-UD5 just to run a single card . Well I say wait for the Radeon 7950 before making your decision. I might be a better value than a GTX 580 or push down the price of the 580 a bit.