In terms of overall gaming performance, the graphical capabilities of the Nvidia GeForce GTX 780 Inno3D iChill HerculeZ X3 Ultra DHS Edition are very slightly better than the Nvidia GeForce GTX 970 4GB.
The GTX 970 has a 4 MHz higher core clock speed than the GTX 780, but the GTX 780 has 88 more Texture Mapping Units than the GTX 970. As a result, the GTX 780 exhibits a 91.6 GTexel/s better Texture Fill Rate than the GTX 970. This still holds weight but shader performance is generally more relevant, particularly since both of these GPUs support at least DirectX 10.
The GTX 970 has a 4 MHz higher core clock speed and 16 more Render Output Units than the GTX 780. This results in the GTX 970 providing 17 GPixel/s better pixeling performance. However, both GPUs support DirectX 9 or above, and pixeling performance is only really relevant when comparing older cards.
The GTX 970 was released over a year more recently than the GTX 780, and so the GTX 970 is likely to have better driver support, meaning it will be more optimized for running the latest games.
Both GPUs exhibit very powerful performance, so it probably isn't worth upgrading from one to the other, as both are capable of running even the most demanding games at the highest settings.
The GTX 970 has 1024 MB more video memory than the GTX 780, so is likely to be much better at displaying game textures at higher resolutions. However, the overall memory performance is about the same.
The GTX 780 has 73.2 GB/sec greater memory bandwidth than the GTX 970, which means that the memory performance of the GTX 780 is much better than the GTX 970.
The GeForce GTX 970 4GB has 1664 Shader Processing Units and the GeForce GTX 780 Inno3D iChill HerculeZ X3 Ultra DHS Edition has 2304. However, the actual shader performance of the GTX 970 is 2646 and the actual shader performance of the GTX 780 is 2500. The GTX 970 having 146 better shader performance is not particularly notable, as altogether the GTX 780 performs better when taking into account other relevant data.
The GeForce GTX 970 4GB requires 145 Watts to run and the GeForce GTX 780 Inno3D iChill HerculeZ X3 Ultra DHS Edition requires 265 Watts. We would recommend a PSU with at least 500 Watts for the GTX 970 and a PSU with at least 600 Watts for the GTX 780. The GTX 780 requires 120 Watts more than the GTX 970 to run. The difference is significant enough that the GTX 780 may have an adverse affect on your yearly electricity bills in comparison to the GTX 970.