Looking at the advantages, the 7800xt has:
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10% lower price
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4 more gigs of vram
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6% better raster performance.
The 4070 has:
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Better frame gen
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Better upscaling via dlss
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Better drivers
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Better rt performance
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CUDA for the few people that actually need it.
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Better power efficiency.
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The ability to use both dlss and fsr. If a game just has dlss, amd users are screwed.
All in all I think the AMD card is still the underdog based in advantages and needs to be at least 15% cheaper in order to sway buyers to team red. For just a $50 price difference, the team green advantages are too stacked imo.
Edit: this is of course in the US market. Every market is different.
This is what finally swayed me to get a 4070 over 7800xt. Coming from great experience with my 5700xt I was excited to get the 7800xt but with a promo that dropped the 4070 by $50 it was too tempting to try the Nvidia features for this generation with the games I play. I still think the 7800xt is a great card but have no regrets so far.