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.
Frame gen has a minor benefit on such a weak card (and AMD has an equivalent), DLSS was so near to indistinguishable from FSR in Alan Wake 2 that most people won’t care, better drivers is fair, better RT is fair (though it still isn’t super compelling in this performance segment in general), CUDA is 100% a plus, power efficiency is 100% a plus, and there’s an FSR patch for DLSS only games (DLSS unlocker). So, in conclusion, a few of your 4070 “features” are kinda weak motivators.