DNC can do a bunch of instant-cast support-related things with their TP, which is why it makes such an effective melee sub. Since melee jobs will be damaging enemies effectively and racking up TP at the same time, and then just fire off some instant /DNC move to heal themself or debuff the enemy or something. They also get a free (doesn't even cost TP), instant-cast self sneak and invis at the same time. (Though iirc, it doesn't last long.) There's not too much more to say about the job, but that alone is enough - there's a *lot* to be said for TP-based support abilities, and even more to be said about instant casting.
SCH's unique spells are the weather changing things and the special helix DoTs (which have the per-tick DoT damage based on how much the DoT lands for like a nuke, so if it lands for 10 damage it'll do 10/tick; if it lands for 50 damage it'll do 50/tick, etc.).
However, they also have a variety of job abilities to do neat stuff like aoe any spell they can get their hands on, reduce casting time, reduce MP cost, boost skills to the level of a B or so *main job* (even if subbed, thus a SMN/SCH can get 250ish enfeebling and actually *land* subjob enfeebles, for example). And, more applicable to SCH main than sub, they can play with their abilities to get at the majority of white and black magic spells (though not all at the same time).
They also get Sublimation, which is kind of like a self-only mini-Refresh/Convert - drains away up to 25% of your max HP at 2/tick (3 with AF) and stores it, and then you can use that (either when full at 25% max HP, or, if you choose, sooner) to get that much MP restored to you. And Sublimination is subbable. Sublimation doesn't stack with Refresh, but it does stack with Ballads and Evoker's Roll.