http://www.newegg.com/Product/Product.aspx?Item=N82E16814202025
ATI Radeon 7870 1GHZ edition. Solid card will serve you well and you can rock out ultra on everything if you are running reasonable resolution of 1080p or 1920x1080. In some VERY demanding games you might need to turn anti alising off. You also get 4 games with it and in my book that's a keeper. IT will run faster than GTX 660 even the clocked edition, however you will not be able to take advantage of physx.
Now if you want Nvidia i would recommend http://www.newegg.com/Product/Product.aspx?Item=N82E16814127699.
The nvidia card is also very solid will also max everything out. IT has better drives and i find it to be more stable but it's personal preference. U will get 1 game with it but it is metro last light which is amazing. THis card will be able to run physx. However keep in mind that activating them will DRAMATICALLY reduce your performance. Now batman arkham city is very physx game and as such favors nvidia. And also it looks stunning with physx i assure you.
Now the choice is up to you. But if you do not want physx and generally want the better POWER for your money i would go with the Radeon 7870 because hell it has 4Games and it's faster then the GTX 660. Physx will not change the way you view a game even though they look good. Mostly it's flags on the ground random background damage like board falling off in batman. Tassaltation seems to be better with ATI which is present in metro last light heavily and many other games.
Personal choice would be the 7870. But i leave it up to you. Both cards are slightly above your 200 budget but. Man up and give 20 more for a better card.