From what I could find on the subject...
Monofilament stretches, and absorbs water, but it is these qualities that may make it worse. The site I found said that it can lose as much as 15 percent of it's breaking strength when it is saturated. It is known for having low memory and ease with tying knots and general handling. The stretchiness of the line is both good and bad... It is looked good to kind of absorb some of the shock of a hard strike of a fish that hits the lure. But the disadvantage of this is that some fish don't strike very hard, you are sometimes not sure the fish are even there, so they can bite on, but let go before you even know they are on. Another thing I found on the website is that the line weakens considerably after long exposure to UV light. Less memory, strong, stretchy (good and bad), easy to handle and tie knots, also abrassive resistant.
Basically sums up the good for monofilament.
The fluorocarbon tippet or line is known for it being nearly invisible to the fish. This is because of less light refracting when it goes through the line... this is probably due to coating or whatever they do to the line. The website goes into some numbers that I don't really know anything about, but the refractive index or whatever it is called is closer to that of water than the monofilament line, this helps it seem less visible. The fluorocarbon line is not stretchy, being rigid, so there is more memory... But with a leather wallet you can straighten that out pretty easy
It is not porous, and has a harder finish, as stated above. This means that it is heavier than water, and will sink because it has no pores to allow air bubbles to attach and keep it afloat. The hard coating means that it is more abbrasion resistant, but retains much more memory. It also helps to keep the rated breaking strength relatively the same whether wet or dry. In most cases, it is the same size or smaller than the same comparable strength of monofilament line, because of being harder material. So it has better sensitivity and hook setting ability. Also it is less susceptible to UV light and chemicals or abbrasion.
Sinking, harder, retains more memory, tough, nearly invisible to fish, more sensitive, better hook setting, but more expensive.
Highlights of fluorocarbon lines.
Hope this helps, I didn't really know what the difference was before looking it up, so thanks for teaching me something in the process! haha
Here is the link
to the website I got the information off of in case you want to look at it, because I'm sure there are some things that I probably didn't explain the best...