for the power requirement of RX 580, you can have the performance of GTX 1070
😉
the FreeSync/G-Sync is not needed when you have a hardware that can push enough FPS.
Since you have an i7, there should be no problem with FPS drops. With GTX 1070, games will run well above 60FPS.
The closest thing that AMD have is RX Vega, which uses more power than your PSU can do.
You should look for a card with a single PCIe power connector up to 180w TDP. since your PSU have only 6pin connector and GTX 1070 (and some 1060) use 8pin, you can use this adapter
https://www.amazon.com/StarTech-Express-Power-Adapter-PCIEX68ADAP/dp/B001TK3TJY
your PSU is still good to carry it.