This response may end up as a long read, I did a lot of research on fishing line last year. What follows is a condensed versions of what I have learned.
First of all lets break down line into a few categories that will enable an easier comparison of the available fishing lines. There are braids, monos, floros, copolymers, and hybrids. These lines are all manufactured for different applications, and in all honesty for most weekend anglers all we need is mono. But lets take each and break down the benefits and drawbacks.
I will start with Monofilament line. This is the line most of us grew up with, it is the one we know the most about and have the most experience with. All mono is is a single type of nylon compressed into a thread. What many people do not know about mono is that it has an open cell construction, meaning that the line will absorb water, as it absorbs water the line weakens as much as 30 percent. This is best illustrated by watching you line, rig up a senko on mono cast it out and watch the line, the first few casts the line sinks slowly, with each consecutive cast the line sinks a little faster, the more water it absorbs the faster it sinks. The more it absorbs the more it stretches. Higher grade mono stretches less than cheap mono, but it all absorbs water, this can be offset by using a line conditioner. Another negative to the open cell construction is sensitivity, closed cell construction aids in sensitvity as the vibrations are not as suseptible to be lost to the water column.
Next is Copolymer lines, which typically is not a nylon floro blend but rather a blend of two or more different types of nylon. The manufacturers can specialize a nylon line that is more abrasion resistant, less memory, smaller diameter, etc, by manipulating the types of nylon. In the end though you have a line that is the same as mono, it has open celled construction, absorbs water, weakens with use, the wetter it is the more it stretches, and will break down in uv light.
Hybrid lines are just that a hybrid of nylon and most of the time floro. IMO these are the lines you want. Floro is basically the same thing as teflon, so it is slick, which is why floro has such bad knot strength. Anyway back to hybrid lines, all hybrid lines are not equal, many manufacturers just coat there basic mono with floro and call it a hybrid. This does nothing to enhance the quality of line other than make it closed cell so it will not absorb water. IMO true hybrids actually intermix the nylon and floro on a molecular basis, such as yo-zuri, the benefits of this are numerous. You get all the benefits of mono and most of the benefits of floro. Examples include, superior knot strength (especially when compared to floro), better abrasion resistance, lower visibility than regular mono (although not the same refractive index of regular floro), does not break down in uv light, better sensitivity, closed cell construction, etc
Now for straight floro, the first myth that needs dispelled right away is the floro doesn't stretch. Floro stretches as much as mono, sometimes more according to test conducted by the tackletour guys. The main benefit to floro is increased sensitivity and a refractive index almost the same as water. All that means is that floro almost disappears in the water. The main drawbacks to floro are lots of memory, poor knot strength, poor performance in cold water and cost. If you get a bird's nest in floro and the line kinks any at all, it must be stripped and replaced, this is the biggest issue I have with hybrid lines and floros, and nest that would not affect mono destroys the strength of floro. The memory issue can be controlled by using a line conditioner.
The final line is braid, braid is extremely strong for its diameter, it does float however which makes it a poor choice some topwater applications, as many people report an issue with the line fouling in the hooks. Braid is solid and IMO stands out in the water like a sore thumb. Tackletour also did some research on this issue and fish would routinely avoid the braid and swim into floro line, the hypothesis is that the fish could see the braid and avoid it and could not see the floro and hit it. Braid has less stretch than anyother line, is abrasion resistant, but cuts easily on sharp objects like rocks, shell banks, etc, but is superior in wood. Braid is extremely sensitive, unaffected by uv light, and does not absorb water as readily as other lines.
So in short after considering all of this what is an angler to do? Many on this forum swear by yo-zuri hybrid line (I'm one of them), it gives you all the benefits of floro and mono at reasonable prices. It is extremely strong for its diameter, 6lb (.01) test average break strength is 11.9, 12lb (.013) test average strength is 20lbs. Is virtually invisible underwater, has closed cell construction, very sensitive, many report memory issues with this line, I treat mine with KVD line conditioner and have no issues. It is a great product and the best part is one line covers all applications. Good luck to ya