Nothing, if less power usage is really a factor. The 2060+-s and 5700 both use similar \ more power per the Techpowerup AVGs. They give us more performance for the added power but offer no magic in terms of efficiency.
The 1660 Ti is what you are after. It varies between roughly 10% slower to 10% faster than a classic 1070.
The 2060 card would be your next option to approach 1080 performance levels but it uses almost as much power as the 1080. So not really what you asked for but next closest thing.
The 1660 Ti may not reach 1080 perf levels but that said, it still pretty much ticks all your boxes. Of the other options: the Radeon 570 is way too slow, it's nowhere near 1070 perf. The Radeon 580 is STILL way too slow for what you asked for AND uses too much power.
redneck 1060...at 2138 core 2124 memory...think about as how I had it...that first bead is jumped and 12.6v. That's up to you both of those new things are alien and wayyy better.