The Corsair SF450 can handle a 1080 and 1600x no problem. If you are wanting more overhead the SF600 is also very good. I have run the SF450 with a Founders 1080 , Ryzen 1700 as well as 2600 with great results. Currently using the SF600 since moving to a Vega64 as its a thirsty card if you let it do what it wants! Ryzen 2600 is the cpu.
7 year warranty on Corsair SF psu as well. Nice piece of mind.
I have used Outervision's PSU calculator for years and it seems decent. With the GTX 680 you may just want to jump to a 600w PSU. The 1080 is way more efficient and would be fine on the SF450.
https://www.newegg.com/Product/Prod...gnorebbr=1&cm_re=sf600-_-17-139-155-_-Product
https://www.newegg.com/Product/Product.aspx?Item=N82E16817139156&Description=corsair sf450&ignorebbr=1&cm_re=corsair_sf450-_-17-139-156-_-Product
https://outervision.com/power-supply-calculator
The 1080 is more efficient, but is only rated at ~15W less than the 680, which has a TDP of 195W. Given that the 680 lacks GPU Boost, it won't have the power draw spikes of newer architectures either, but on the other hand it's more likely to utilize its full TDP even at relatively light loads. Also, how TDP is defined has changed quite a few times, so YMMV. Still, any PSU suitable for the 1080 ought to be suitable for the 680 as well.
Most people buy massively overpowered PSUs, which I believe is a remnant from the olden days when PSUs were generally garbage and quality was unheard of; you had to buy overkill to ensure it didn't die under load. These days, PSU ratings are often conservative, with many units from reputable brands being entirely capable of running above their rated output for hours and hours and hours with halfway decent cooling.
A 1080 and a 1600X should pull noticeably less than 400W while gaming, and you'd have to OC them heavily to come near 450W. My 1600X + Fury X system runs around 410-440W at the wall under load (with a 750W 80+ Gold PSU (I had a more power hungry CPU when I bought the PSU, 550W would be plenty today), so that translates to ~400W output from the PSU), and my GPU should consume ~100W more than any stock 1080.
Check out
AnandTech's 2080/Ti review:
That's full system power consumption
at the wall with an i7-7820X (8c16t, 140W TDP) and quad channel memory. In other words, a switch to a 1600X would lower those numbers by a noticeable amount.
Of course, running a PSU at near its rating for prolonged periods is bound to wear it out quicker than running it at half capacity, but with a 7-year warranty, I wouldn't worry. The biggest thing would be fan noise, but a higher rated unit in the same chassis with the same fan (like the Corsair SF600 vs 450) will still produce roughly the same heat and thus run the fan at roughly the same speed, so that point should be moot.