While I agree that Nvidia currently has the best options in the $200-$300 price range, the RX 580 is now in a somewhat lower price range, so it's not an entirely fair comparison. The RX 580 is now a more than 2-year old design, and an 8GB model can be found for as little as $160 after mail-in rebate, or $170-$180 without. However, I would not consider that card as a worthwhile upgrade for you for 1440p, as it is only about 15% faster than your RX 570. It has been directly competing with the GTX 1060 6GB, not the newer 1660. The RX 590 is about another 10% or so faster, but it's effectively just a minor update of the RX 580, and is also probably not worth your time, as it is priced too close to the somewhat faster and much more efficient 1660.
As I pointed out before, a 1660 would probably the absolute minimum I would consider for 1440p gaming right now. At that resolution, it should perform roughly similar to how your RX 570 performed at 1080p, or about 30-35% faster with both cards running at the same resolution. Which isn't exactly ideal, and you will likely need to turn down some graphics settings to maintain over 60fps in some of the more demanding games. A 1660 Ti, in turn, provides around 15% more performance than a 1660, and will be more likely to keep most newer games above 60fps at 1440p while still keeping graphics settings high, which probably makes it a better option. And if you want some room to grow for future games, or want to push somewhat higher frame rates on a 144Hz screen, it might be worth moving up to the next performance tier above $300, with something like an Nvidia RTX 2060 or 2060 Super, or an AMD RX 5700 or 5700XT, which just came out today.
AMD has just started releasing their new generation of graphics cards, and they are looking rather competitive so far, but at this time they have only released those cards priced at $350 and above, and have not yet announced any cards in the sub-$300 price range, so it could potentially be some months before they have really competitive products priced similar to a 1660 or 1660 Ti.
That's probably more down to the manufacturer that built the card rather than AMD or Nvidia. While AMD designs and supplies the graphics chip and sets specifications for a card, the card manufacturers (like Asus, Gigabyte, MSI and so on) are responsible for building the cards and selecting other components. Much like a motherboard, they are building the board that the processor plugs into and designing its cooling system. Most of those manufacturers will produce both AMD and Nvidia cards. And of course, hardware failures can occur with all brands of cards.