My budget is 100 dollars. My main goal is BF3 on high/ultra settings with decent frame rates. I know both cards are outdated but my budget is really tight and need something better than integrated for gaming.
You will not get to ultra on BF3 with those 2 cards. I had an HD 5850 in the past and even that lagged and could not handle BF3 ultra on 1080p with 64 people in a map with rocket blasts in a metro map.
If power and heat are not an issue, then the GTX 480 is a nice buy and a very powerful card. As far as they 560, I would recommend the 560 Ti instead. It's a little more powerful for not much more money.
Or maybe http://www.newegg.com/Product/Product.aspx?Item=14-130-660&SortField=0&SummaryType=0&Pagesize=10&PurchaseMark=&SelectedRating=-1&VideoOnlyMark=False&VendorMark=&IsFeedbackTab=true&Page=2#scrollFullInfo
buy the 480. Its will probably give you the best performance.