I use this fantastic website: https://www.userbenchmark.com/
It compares multiple benchmarks from people's rigs all over the world, and is the most accurate component comparing website I know. You can compare GPUS, CPUS, SSD, HDD, RAM, and USB devices. You can also benchmark your entire system here and compare it to others with the same specs.
It includes details like percentiles and percentage performance compared to others. It also includes popularity and sales stats.
This should hopefully help you make your decision and give you more piece of mind when it comes to picking PC parts.
To answer your question also, the RX 580 is better than the 1060 3GB. Not only does it have much more VRAM (which is great for future-proofing), it also supports every free sync monitor with HDMI (free-sync is much more common than G-sync and cheaper).
If the RX 580 is a similar price to the 1060 3GB, then get that. Both cards will provide you with a great 1080p 60-fps high-ultra experience in most games, but the lack of VRAM in the 1060 will hold you back. As for the 1060-6GB, It performs very, very similarly to the RX 580 and is certainly not worth the extra $50.
The decision is yours, but I would take the RX 580 based on your pricing claims.