The benefits of flourocarbon lines/tippets are twofold.
First, the material, due to it's 'refractive index' is supposed to be invisible underwater. The concept is that it 'refracts light' the same as water does, so it blends in and can't be detected against the water.
Second, the material is denser than regular monofilament and thus sinks faster. Makes it nice for subsurface techniques, but beware of this if you fish with dry flies a lot. It doesn't 'float', so you will have to rely on surface tension to hold it up....applying floatant to it kills the whole 'invisible' thing, but for dries it probably doesn't matter....if they don't care about that little line made by the surface of the water to the line interface, then they don't care....
Another minor benefit is that it doesn't degrade in sunlight or heat like mono does.
So, while I agree that the tippet stuff is a 'different' formula and is stronger for a given diameter than flourocatrbon 'line', I do question whether or not it matters.
If you would normally use 4x 'mono', then the idea behind flouro is that you could use 3x or even 2x flouro in it's place, since it's 'invisible'. It lets you use a 'stronger' or 'thicker' tippet without it being visible to the fish.
If you use 6# breaking strength flourocabon line in place of 4x tippet, then it's pretty much a wash. Sure it's 'thicker' but it's also 'invisble'.
If all you want is thinner and stronger and you are willing to pay for it, then by all means use the flourocarbon tippet material. Also, not all flourocarbon tippet is equal. Some 'tippet' brands list significant difference in diameter to breaking strength ratios compared to other brands. Make sure to look carefully before making a purchase.
But there is no reason not to use flourocarbon line either, as long as you don't mind a bit of extra 'diameter' to get to a given breaking strength. Since it's 'invisible', it won't matter to the fish, they can't see it.
I've found that I can get away with 8 pound flourocarbon 'line' (I'm using a Cabela's house brand stuff) as a level leader behind my sinking line while streamer fishing for trout in stillwater. 8 pound line is plenty heavy enough for even the largest trout I'll face and it saves me from breaking off too many flies. It gives me some chance at the occasional large pike that happens along as well. The fish don't seem to mind it a bit, since it's 'invisible', they can't see it. We catch almost an obscene number of trout each summer.
I'm using a long section of 4 pound 'Vanish' as a tippet for deep chronimid fishing, and again, the fish don't seem to care a bit. Sure, it's thicker than 5x flouro, but it's invisible, so why does it matter?
For subsurface bass fishing in our clear water lakes, I use the same 8 pound flouro line for a tippet. The bass don't care, since they can't see it. Still catch a lot of them.
I have a lot of the Frog hair and Rio flouro tippet that I use for streams and rivers like the San Juan and the Animas. It's 'thinner' so it gets down faster in the current.
Good Luck!
Buddy