Right now ATI has the upper hand, with its new DX11 cards being (finally) widely available and prices for the 'old DX10 cards falling, the Nvidia products tend to be more expensive for their performance, or just a generation old.
If you want DX11, right now the only card within budget, and available, is the HD5770 but it is not quite as fast as the DX10 generation cards in the same price bracket.
For the same money, give or take, you can get a faster HD4870 but if you chose to go that way, be quick, stocks are dyring up quickly and that card, along with the GTX260 has NO DX11 capabilities at all:
One thing you have not mentioned is if your motherboard supports SLI, if it does your best option might be the GTX260 with the 8600 used as a dedicated PhysX card in the second slot.
If the motherboard does not support SLI there is not enough performance difference to seperate the HD4870/GTX260, either will be a huge upgrade and neither will dissapoint.
For a personal recommendation: HD5770, while not quite as fast as its DX10 predecessors it's no slouch either and shines at your resolution. It also draws less power (big hug to the Earth) and is almost totally silent with the stock cooler.
Final point: Nvidia should be releasing their new cards later this month. I strongly suggest you wait rather than making a decision now.
Given that you have not given any price/s for a HD5770 I'll assume they are expensive in your part of the world (which is?). For my money the HD4870 is the best buy, though, especially if it is the 1Gb version.
GTS 250 can be had for $100 all over the place in the US.....the 260 was $155 (US) when the 5770 came out ...... now it's been driven up to over $200 and tho it and the 4870 outperform the 5770 by 10% in DX9/10 games, I don't think it's worth the extra $45. Here's the 250 for $100 from solid vendors.