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.
Because at just 10% the 4070 is the better buy. With the current prices the only time I would recommend the 7800xt is for 4k gaming, where the 16 gigs of vram can actually make a difference, but tbh neither of those cards are 4k cards. They shine at 1440p. Why lose all the nvidia features for just $50? It makes no sense.