In terms of overall gaming performance, the graphical capabilities of the AMD Radeon HD 7850 XFX Core Edition are very slightly better than the AMD Radeon R7 260X Sapphire 2GB OC Edition.
The R7 260X has a 290 MHz higher core clock speed but 8 fewer Texture Mapping Units than the HD 7850. The lower TMU count doesn't matter, though, as altogether the R7 260X manages to provide 9.4 GTexel/s better texturing performance. This still holds weight but shader performance is generally more relevant, particularly since both of these GPUs support at least DirectX 10.
The R7 260X has a 290 MHz higher core clock speed than the HD 7850, but the HD 7850 has 16 more Render Output Units than the R7 260X. As a result, the HD 7850 exhibits a 9.1 GPixel/s better Pixel Fill Rate than the R7 260X. However, both GPUs support DirectX 9 or above, and pixeling performance is only really relevant when comparing older cards.
The R7 260X was released over a year more recently than the HD 7850, and so the R7 260X is likely to have better driver support, meaning it will be more optimized for running the latest games.
The R7 260X has 1024 MB more video memory than the HD 7850, so is likely to be much better at displaying game textures at higher resolutions. However, the overall memory performance is about the same.
The HD 7850 has 54.4 GB/sec greater memory bandwidth than the R7 260X, which means that the memory performance of the HD 7850 is much better than the R7 260X.
The Radeon R7 260X Sapphire 2GB OC Edition has 896 Shader Processing Units and the Radeon HD 7850 XFX Core Edition has 1024. However, the actual shader performance of the R7 260X is 927 and the actual shader performance of the HD 7850 is 793. The R7 260X having 134 better shader performance is not particularly notable, as altogether the HD 7850 performs better when taking into account other relevant data.
The Radeon R7 260X Sapphire 2GB OC Edition requires 115 Watts to run but there is no entry for the Radeon HD 7850 XFX Core Edition. We would recommend a PSU with at least 500 Watts for the R7 260X and a PSU with at least 500 Watts for the HD 7850. The two GPUs have been recommended a PSU with the same amount of wattage. As such, there is no need to worry about which will more significantly affect your yearly electricity bills.