Hard fluorocarbon
Hard fluorocarbon is a variant of conventional fluorocarbon, with a very hard, tough material. It offers unrivalled abrasion resistance, but also has its drawbacks. Its stiffness makes it difficult to use for certain techniques requiring suppleness in combat. Connecting knots with braid also tend to slip, as the latter doesn't always manage to bite into the fluorocarbon material if it isn't fine enough. In fact, some knots are very difficult to tie and tend to slip once under tension.
Hard fluorocarbon is therefore used in very few circumstances, although it is indisputable. It is mainly used for anti-cutting line heads for pike fishing, since its abrasion resistance prevents it from being damaged by fish teeth.

Nylon
Nylon is the leader most used by most anglers, as it is both practical and inexpensive. Its main advantage is its flexibility, both when pulled and when you try to bend it. Connecting knots with nylon often go very smoothly, as the braid can easily pinch it and thus tighten very tightly. However, its main disadvantages are its low resistance to abrasion and heat. Low abrasion resistance may not be a problem when fishing in rocky areas, but sensitivity to heat requires good knots if you don't want to lose all the initial resistance.
Nylon is mainly used for trout fishing in rivers, where suppleness and elasticity are important. It can also be used for surface lure fishing for black bass and perch, to limit jerks when a fish jumps after casting and avoid stalls.

Super soft fluorocarbon
Super soft fluorocarbon is a good compromise between nylon and hard fluorocarbon. Its resistance to abrasion is superior to that of a nylon, while allowing you to easily make solid knots that don't slip or become as brittle with heat. It can be used for pike fishing (as a leader before the anti-strike leader), as well as for pike-perch, perch and black-bass fishing.
Obviously, you lose a little abrasion resistance compared with hard fluorocarbon, but the advantages more than make up for the difference. Quite simply, this is the most all-purpose leader, which you can of course change in the specific cases mentioned above.