If you can buy GTX 770, then buy that one. SLI is better than Crossfire and GTX770 uses less power. Between these cards the performance will be 7-8% different, GTX770 i almost 7-8% high as compared to R9 280X. R9 280X is close to GTX770. If you can't buy GTX 770 then go for AMD.
I've had a GTX 770 and now I have an R9 280X. The 770, like stated above, will get you better FPS, almost across the board. But the R9 280X has more memory and more shaders. My Shadow of Mordor looks better but slightly less FPS. Anyhow I've overclocked my 280X and I'm very happy. I run dual 1080p monitors as well. The only other card in this price range is the 4GB GTX 960 but it's less powerful than both the 770 and 280X.
Yup, RCFProd you can't buy it under 240$. If you have proper cooling system for over-clocking and not have much budget to buy GTX770 then take R9-280X, its also a good card and over-clocking R9 280X will leads to little more close frame-rates to GTX770.