They're close to each other, both in the price range and performance as you can see here:
https://gpu.userbenchmark.com/Compare/Nvidia-RTX-4070-vs-AMD-RX-7800-XT/4148vsm2184033 and
https://www.techspot.com/review/2736-geforce-rtx-4070-vs-radeon-7700-xt/. The latter has a typo in the address. One more thing to consider is the power consumption, the Radeon is about 20-25% thirstier but it also has more memory.
RTX isn't as good on AMD cards as it's on Nvidia cards but if that's not of importance, both are top shelf products. Not flagship but competitive performers in a decent price range. I guess there's going to be some price competition in the near future between the two.
I'd say the choice should be done by the price and your monitor: If your monitor (or VR) supports GSync Nvidia might be a better choice, if FreeSync then AMD.
