As an example.
Fluorocarbon allows a greater amount of natural light to pass through it whereas monofilament tends to refract light.
Underwater fluoro is less visible and sinks easier.
Great for subsurface.
Mono naturally has more buoyancy and refracts light. This is great on all accounts on the surface film, which it allows my flies to float higher and also is laying on top of a film that is refracting light already. I believe this makes it less visible than when it is subsurface.
That said, while I know fluorocarbon line won't sink my dry fly, you will never convince me it can make a let's say Elk Hair Caddis, ride as high and as long as mono.
Everyone has probably heard the claim that because fluorocarbon is more dense (1.78) than nylon (1.1) then it will sink faster. While this is true, what you rarely read are the actual sink rates and their subsequent practicality.
According to the BIB article “If you take two pieces of line, one nylon monofilament and one fluorocarbon, sink them in a column of water and time their drop rate, what you’ll find is that it takes the nylon monofilament about 45 seconds to drop 30 centimetres (12″) in the water column. A similar piece of fluorocarbon will make that same 30 centimetre (12″) journey in about 15 seconds, still 3 times faster than nylon but not overly fast in the big scheme of things. If you think of your average cast and retrieve taking somewhere between 30-60 seconds, under its own accord the fluorocarbon will have only had the chance to move 60 – 120 centimetres (24″ – 48″) down into the water column in that time period.
Only 15 seconds to sink 12 inches or 45 seconds to sink 36" between your rod tip and the fly is a good way to get micro drag on some waters. In dry fly applications I'll pass on fluorocarbon.
YMMV