The R9 270 can give you an average of 45 fps on 1920x1080, around 50 on 1680x1050 and that's with ultra settings in bf4 (which gives you an overall view for all high end games). I'd say you would get a smooth 55-65 fps on your preferred resolution, which is quite playable
Although it is not guaranteed as those results were made with a quad core processor, which is really needed in new games. And your i3 2120 would really be a bottleneck for the R9 270.