I find my clip on sunglasses are very useful for cycling. They give me the glare protection I need and they also help to protect my glasses from being scratched by flying objects when I cycle. That's quite an important factor when your glasses have varifocal lenses which cost over £250!
I have both spring-fit and flip up sunglasses and have tried both types when I'm out cycling.
Having said that, I tried wearing my flip ups on the day shown in the photo, which was quite blustery - a cross wind of about 12 knots - and the flip ups stayed in position perfectly. They have the advantage that you can flip up the lenses when you cycle through a shaded area, and you can even use the tinted lenses as a shade from overhead glare when cycling into sun by flipping them up halfway.
In terms of lenses, my preferred choice for summer cycling are the brown ones. They filter out the very bright sun, and the polarisation cuts reflected glare very effectively. Brown lenses also increase contrast so you get a clearer view of what's ahead.
For autumn and spring cycling I prefer to wear the copper tinted clip on sunglasses. They block less light, while increasing definition and contrast.