So as far as I'm aware, shotguns in crucible only got their perks nerfed while they took a 45% damage reduction against AI. I'm assuming that means 45% away from the current damage, so that makes it only slightly better than the original vanilla damage. (It sure feels that way too.)
Will you still use shotguns in PvE now? I probably still will but more for fun and probably not on serious endgame activities. My point-blank shotgun shots deal the same or less damage as my Benevolence now, so why risk getting up close? They still are great for bum-rushing non-major enemies, but majors just eat up the buckshot now.
EDIT: Please remember this topic is all about PvE shotgunning. I haven't noticed much difference in PvP with them.
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They'll still be effective, just not effective enough to trivialize encounters with majors