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So for the RTX 3060, you're looking at, closest equivalent in the RX 6000 series, the RX 6600 XT. And that's two full tiers below the RX 6800 XT. In nVidia's terms the x60 to x80 tier usually doubles performance give or take. Not sure how accurate that is when comparing the RX 6800 XT to a GTX 1080 Ti, though.
The cooling isn't going to have a substantial relative performance difference so it doesn't factor in.