Not sure what you're talking about here. The 8800GTX was the more powerful GPU of the two and it released in before (by a few days) the PS3 did. And it was a by far more powerful GPU than that in the PS3.
I'm fairly sure that in the vast majority of DX9 era games released on both platforms, the 7800 GTX512 (or it's more modern and available equivalent the 7900GTX) was putting in at least as good a performance as the Xbox 360. Obviously once games started to lean more heavily on DX10 and unified shaders those old GPU's wouldn't keep up, but it was years before that started to happen in the PC space.
Give me some examples? Of course the 7800 series was outdated on the PC side by G80, but G80 outdated both consoles too. It outdated everything.
Literally obliterating either consoles performance in virtually ever cross platform game for years. I remember this quite well. That card was a monster despite not having unified shaders. It could literally go head to head with the 7950GX2 in many games and could even give the 8800GTS a run for it's money. This is the 1950XTX but that was only a marginal upgrade over the original and this game is no exception:
100% sure. The XTX was pushing 426 GFLOPS of combined pixel and vertex shader power to Xenos's 216 GFLOPS. The 8800GTX was 518 GFLOPS including the MUL but had many other advantages.
I don't disagree with your core point that the PS4 generation launched in a worse position relative to PC's than the PS3 generation. That's a given. But in pure performance terms PC's were ahead of the PS3 from day 1 by a pretty significant margin. Compared to the Xbox 360 which was a spectacular console the picture is more muddied because in raw performance terms it was theoretically possible to build a single GPU PC at the time that would hold up very well for years against it (but not it's full life). And within 2 months you could build a PC that was definitely more capable for arguably the consoles full life. Then within 1 year the console was severely outdated by the first DX10 GPU, arguably more so than the PS4 was at launch vs the top end PC's of the time.
I do think the current gen is in a better position than the PS4 gen for the record though. Moreso
at launch on the CPU and storage side than the GPU side though. However because the PS4 gen launched mid way through a GPU cycle (which it was already outdated by), the next gen of PC GPU's - Maxwell - arrived faster than this console generations 2nd gen PC competitor - Ada, and offered far better value for money to boot.