Upgrading to an i5-4670/4690 would give you 40-50% better performance in games heavily dependent on single-threaded performance. An i5-3470 would only be 20-30% better.
As for whether your i7-960 would manage to keep pace with a 780, that would depend on the game, resolution, detail settings, etc.
If you are making plans to get a 780Ti and are seeking advice on whether or not to upgrade the CPU/MoMo(/RAM) at the same time, I would say upgrade the GPU first and if you do not get as much of a boost as you expected due to CPU bottleneck, upgrade the rest since you were planning to if necessary anyway.
This way, if the GPU-only upgrade makes you happy for a while longer, it might tide you over to Broadwell or Skylake which should be...