I won't be shocked if AMD doesn't adjust prices like at all, at least initially. I expect their first move to be a game bundle promotion or something. But even then, I feel like you'd have to be silly (or AMD have some bombshell that will radically change things) to go for Navi over the Nvidia Super cards. And the thing is, even if AMD drops the price some, Nvidia can likely hit them with a double whammy of firesale on the non-Super RTX cards, and then probably drop prices on the Super cards after that. I'm skeptical that Navi costs AMD less than Turing costs' Nvidia, and on top of that AMD has to weigh GPU sales against possibly losing higher margin CPU production. So I think we'll end up in a relative stalemate, where they'll do some game bundling and maybe some price maneuvering, maybe we'll even see 5700XT drop to $399.
Honestly though, even if the 5700XT was $299 I think I'd pass on it (same with the Nvidia offerings if the 2060 Super were $299 and the 2070 Super $399). Too many questions about ray-tracing for me to care much about it yet (once its properly integrated, especially with HDR and modern color, lighting, and shadow, it will be worth it). Plus I'd wait for HDMI 2.1 and DP 2.0.
Next year should be a LOT more interesting for GPUs. Nvidia on 7nm (where it sounds like they got a pretty ridiculous deal from Samsung for production so maybe we'll see them be more aggressive on pricing), Intel should be in the market (they might be aggressive on pricing to gain marketshare), and then we'll have a better idea of what AMD is doing (AMD should have a tangible start towards ray-tracing support; we'll likely get a lot better idea of their GPU plans).
Are you sure it's more advanced? AMD has features (though we won't know how well they work until reviews) that you can use in more games sooner with less of a performance hit.
Unless AMD has been seriously sandbagging, they don't have anything that Nvidia likely doesn't already have or could implement. Nvidia already has some sharpening options (specifically for gaming, there's a tab in their drivers that has a bunch of that type of image tweaking options; and they definitely could implement the sharpening that AMD is doing; they claim they already offer what "anti-lag" is as well). There's some slight chance that AMD might have a more advanced video processing block but I doubt most people would buy for that, and I'm not sure its true. Nvidia's encoder has better software support so even if its superior it doesn't mean anything if the software you use doesn't support it.