Hi Tyrant
For you to choose over a Graphic Card you first need to look at the GPU Core Speed and the Stream Processing Unit
These two is the major factor of the performance when you playing your Games
Basically the Sapphire HD7850 is slightly better then the R7-260X
here is the link to R7-260X specs:http://www.sapphiretech.com/presentation/product/?cid=1&gid=3&sgid=1226&pid=2071&psn=&lid=1&leg=0
And here is the HD7850 :http://www.sapphiretech.com/presentation/product/?cid=1&gid=3&sgid=1160&pid=1654&psn=&lid=1&leg=0
you can compare yourself for these two cards
Also,keep an eye on the Overclockable potential of the two cards
Well i cant say for sure for the new R7-260X card because i didnt owned it nor i did any research yet on the R-series card
but for the Sapphire HD7850 which i currently owning, I overclocked it from 920MHz(Mine is 2GB OC version) Core Clock to 1050 MHz and Stream processing Unit from 1200MHz to 1450MHz with power supply +20%
Also,pay an attention on the Buswidth
Sapphire HD7850 has 256-bit GDDR5 buswidth while R7-260X has only 128-bit which is half of the HD7850
Buswidth is consider as the pathway for the processed data transfering speed in the GPU.It represents the bridge in real life
Imagine when you at a big bridge,more people can cross over the bridge at the same time if the bridge is wide:However when the bridge is narrow and can only allow one person to cross at the same time,then the time needed for the people to cross the bridge will be longer.This concept applies the same as the Buswidth
Hope i helped you