I second GTX 1660 from between the two. Reasons: Newer architecture (Turing 2018 vs Polaris 2016-17). 1660 is much faster than 580 in everything. IMO, 1660 super or ti are good deals if available around 20k. RX 580 is a good deal only if it drops at 12k levels, which it wont.
For 4k gaming, you ideally need a lot of hardware power. What is the rest of your system specs? Anyhoo, the minimum 4k cards are RTX 2060super or RX 5700 (4k low to medium). RTX 2080 super and ti for 4k med-high. And since you are out of touch, let me help you with approx prices.
TLDR for the gibberish below in case you choose to not read: 4k low to medium needs at least RTX2060 super which is at 33k. Or RX5700 which in India is also around the same price. With a 1660, you can do 4k only on motion pictures. Games will become a nice PPT slideshow. Unless you are thinking of 4k'ing pre 2013 games which may not support 4k in the first place. Sorry brother, but it is what it is. Also, here is and example link to show you how each cards stacks up.
ZOTAC joins the GTX 1660 SUPER launch party with their AMP edition, a compact product with a capable cooler as well being factory tweaked. The SUPER edition card comes with faster GDDR6 memory but rem... DX12: Gears of War 5
www.guru3d.com
GTX 1650 - 12 - 15K depending on where you look. Good for med-high 1080p30 or low-med for 1080p60
RX 570 - now its available at less than 13k making it a very good deal. It will beat the older gen 1050ti in most games and reaches almost 1060 levels. Meaning it performs on par with 1650, so your choice between the two.
GTX 1660 - Available above 15k. Doesnt make much sense. Dunno why it exists. Nvidia made a poo poo here with super series but if I start talking about it I will go on for a couple of hours lol. ANyhoo, 1660 beats 570 and 580
RX580 - Because of the above reason, it should be prices less than 14k for it to make sense. Which will kill 570, so it wont happen. Performance difference between 570 and 580 is less than the price difference between the two. Spending 5K more on 580 does not give you 40% more performance.
GTX 1660 super or ti - Whichever is cheaper, get it. Should be close to 20k ideally, but they are happily selling these cards to us between 20 and 25k.
RTX 2060 - cheapest is 26K. Makes much more sense than 1660 super or ti, because the prices difference is less than the increase in performance. By spending 6k to 1k difference over 1660 super or ti, you are essentially getting 30% performance non ray traced performance
RTX2060 super- around 34k. Makes most sense for 1080p ultra. All games will be at least 60FPS including metro exodus. Majority of games will be above 90 FPS, with many non esports titles touching 120 FPS too. Not a good card if raytracing has to be used as the FPS goes below 60 in all the ray traced games. This is the starting point to even think about 4k gaming at low - med details in new games after 2017. Before 2017 games, 4k med-high settings.
RX5700 - performs on par with 2060, sometimes even beats it
Cards above this are 2070 super (my favorite), RX5700xt (my favorite), 2080 super, 2080 ti from 37k to 1.10 lacs. haha. And if you are confused by all this, blame nvidia for naming their cards like that and AMD for not releasing mid range cards this cycle.