Until now perhaps, with the release of the NVIDIA GeForce GTX 1660 which may be about to change this. So with comparison data between these two cards hard to find I thought I'd post these performance charts for the benefit of others.
The rest of my PC system was upgraded about 6 months ago so this should be a fair evaluation of pure graphics card performance.
Test System
16GB (2 x 8GB) DDR4 3000 (GeIL Super Luce RGB sync AMD Edition )
Gigabyte AB350M-Gaming Motherboard
Palit NVIDIA GeForce GTX 680 2GB (GDDR5*)
GigaByte NVIDIA GeForce GTX 1660 OC 6GB (GDDR5*)
I came across the Final Fantasy XV Benchmark and ran this to get some more comparisons. The score above for the GTX 1660 places it above the Radeon RX Vega and below an NVIDIA GeForce GTX 1070 which are both priced at $300+. For the GTX 1660 you'll pay around $220 and since it's newly released you might see some bundle's pop-up with games thrown in to sweeten the deal. Plus I'm hoping to sell my GTX 680 on eBay for around $60 which will help reduce my upgrade cost.
Performance wise the GTX 1660 should give you about twice the speed of a GTX 680 with additional benefits such as more memory for higher resolutions, lower power usage and support for DirectX 12 over 11. Overall this card seems like a decent upgrade if you've been looking for something faster which doesn't break the bank.