My experience is braid is cool because you can cast a mile with it. Great for long distance. It also does not have memory so you can really feel a direct connection to the end of the line. Braided is slippery stuff. Harder to tie knots in my opinion. Just takes some getting used to. It also seems to make more noise on my guides.
Fluorocarbon is supposed to be invisible. Expensive. Less memory than mono too. Honestly I’ve only used braided and mono for spinning rod. I do use fluorocarbon tippet when fly fishing and what I can tell you there is it is good for wet fly but generally not good for dry fly because it does not have enough memory. More expensive than mono but probably worth it, at least when nymph fishing.