The standard power ratings are:
GTX 980: 165W
RX 580: 180W
That said, while the GTX 980 has a performance edge over the RX580, it's only a small edge.
In any case, I'm assuming that you're looking at a used GTX 980, and a new RX580. I don't know where you're located, but generally used cards don't have any warranty.
If you're only interested in smooth 30fps+ at 1080p, you might consider saving some more money and getting an RX570 then. Its standard power rating is 150W, and while a little slower than the RX580, is still considered good for 1080p gaming.
Here's the US prices for RX570 and RX580 cards, both 4GB and 8GB variants of each, sorted by price.
https://pcpartpicker.com/products/video-card/#c=392,391&sort=price&page=1
Whoever that somebody is, they're full of crap. Different models of AMD and Nvidia cards have greater and lesser performance, and Nvidia's fastest card outperforms (and is far more expensive than) AMD's top card, but that's about it.
I suppose if they meant that Nvidia's RTX cards have ray-tracing, there might be some merit to it, but ray-tracing causes a significant performance hit for that extra detail/realism. But ray-tracing ONLY exists on Nvidia's RTX 20-series cards, not on any of the GTX 16, 10, or 9 series.