On the PSU: From what I can tell, PSU issues are much less likely than they used to be; a lot of the hardware design has had a strong mobile influence lately, reducing power consumption (and resulting heat production). So it actually probably uses less power than a comparable card from previous gens. The 980 and 970 require 165W and 145W, respectively. The specs of the 780 are 250W, for comparison. Very disappointing for those of us hoping to use our PCs as a space heater.
As for the specs:
The 970 and 980 are the same base hardware, created on the same production line; as such, there are no architectural differences, simply a matter of having disabled or tuned down bits in the lower end models (which is good, since we're otherwise comparing apples to oranges)
Same VRAM; textures to high quality will not cause any differences in perf.
The 970 has a slightly lower core clock speed ~7% slower (math operations take slightly longer), however, it has the same memory clock speed (memory operations take the same time). Depending on the code running on the GPU, this may slow it down slightly, but memory access is often the bottleneck in shader code, and quite often the bottleneck in GPGPU compute code. All in all, probably negligible effect from this.
The main difference is the Streaming Multiprocessor (SM) count. The 980 has the full 16 SM units enabled, while the 970 has 13 enabled and 3 disabled. The SM units contain the cores running stuff (128 cores per SM). As such, you can run somewhere around 81% as many threads, and thus is the absolute worst any performance difference between the two could be. Back in the real world, however, this will make less of a difference as you won't be running the GPU at 100% all the time due to overhead ranging from CPU processing delays to memory bandwidth, and as such actual benchmarks put them within a bit lower margin (85%-90%).