In regards to the 580 being a better buy; if you are restrained on budget, look at used cards. there are a metric load of vega 56 cards going for under $200 on ebay right now. Those would be a far better deal then any 580, offering significantly more performance then the 580 or 5500xt. You can find Vega 64s for $230-250, same with GTX 1070s. Hell, the 290x, which slots in between the 570 and 580, can be had for $75-90!
I know the whole meme about "BuT uSeD gPuS" and "BuT mInInG". The last 5 GPUs I've used in my gaming PC have all been bought used for a fraction of the price. My second 550ti, 770s, my 480, my vega 64, all bought used, all without issue. Given how much I've saved, I'd say its well worth it. If I were on a budget, I'd grab an old 290x and wait out the next 1-2 years of GPUs, as the GPUs released early into a console's lifespan dont do very well by the end of said lifespan. With new consoles coming out with more RAM, if VRAM requirements jump significantly again, none of the current da 8GB cards will be comfortable. Why waste your money?