The problem with exotics is that legendary weapons are straight up better than many of them, and with armor is that there is usually one good exotic while all the others aren't nearly as useful.
I guess it kind of depends. As I said, they're generally better than any given legendary at at least some situational encounter. Generally speaking No Time To Explain is worse than any well-rolled legendary pulse. But if it's a Small arms CoE Challenge where you wanna get precision kills, NTTE basically has infinite ammo and will shine. You could paint a similar picture for most Exotics - there will be some place or moment where they're perfect for the job even if they're not fantastic overall or in general.
As for Armor, there's some garbage out there but I think there's multiple good options for every class. On my Warlock I switch between Ophidian, Manacles, Ram, Starfire, Voidfang... on my Hunter I love Shinobu's, Tarantella, Bones, Frost-ees, Graviton, Symbiote... Titans are more limited because of the way I play them so it's basically Garrison or Armamentarium for me, but Saint-14, Glasshouse also have their uses. Again, some are very useful overall and thus get used far more than others, but most will be excellent and optimal in at least some context.