Use my comments as a guide:
http://www.tomshardware.com/answers/id-2499036/gtx-960-270x.html
For RAW PERFORMANCE an R9-280X is a better deal by about 15% if we compare good cards overclocked to max (the GTX960 is weaker to start but overclocks better which works out to about a 15% difference in the R9-280X's favor).
There are other factors in favor of the GTX960:
a) quieter and SILENT for certain models as fans can shut off in light usage
b) MFAA for certain games can add about 15% (varies a lot). More games will get added.
c) other: H.265, voxel lighting support for future games...
The R9-280X however has 3GB of VRAM which may big deal for some upcoming games.
*So pros and cons. If raw performance is most important I'd recommend...