We know exactly what's in the PS5 Pro, because the specs have been made public. It's an RDNA 3.0 GPU with 60 CUs clocked at 2.18-2.35 GHz. The 7800 XT is an RDNA 3.0 GPU with 60 CUs clocked at 2.12-2.43 GHz. It appears to be the exact same processor with a 5% slower clock speed and a ~10% slower memory clock. It's not an RDNA 2.0 GPU like the 6800. One of the key differentiators is raytracing performance on the 6000 series is so bad as to be useless, while it's acceptable on the 7000 series. The PS5 is similar to a 6600 XT, though.
Key specs:
| GPU | RDNA | CUs | Peak clock | Bandwidth | FP32 |
| PS5 | 2.0 | 34 | 2.23 GHz | 448 GB/s | 10.3 GFLOPS |
| 6600 XT | 2.0 | 32 | 2.59 GHz | 256 GB/s | 10.6 GFLOPS |
| PS5 Pro | 3.0 | 60 | 2.35 GHz | 576 GB/s | 33.5 GFLOPS |
| 7800 XT | 3.0 | 60 | 2.43 GHz | 624 GB/s | 37.3 GFLOPS |
So no, you're not building a "PS5 Pro Killer" with a $300 GPU. I wouldn't consider a marginally better GPU to be a "killer," which is why I said a 4070 Super or something in that tier.