I'm just going to throw my own little observations in, and I'm going to throw some monkey wrenches in with them.
I am dual specced in Destruction and Affliction. I am in ilvl 564 gear, nothing Mythic (mixture of LFR/Flex/Heroic T16 pieces). I have my legendary meta and cloak, and I have the Heroic Hellscream's Warstaff heirloom weapon. My gear has always been obtained with the loot specialization set to Destruction, and I'm gemmed and enchanted for Destruction. However, I notice that when switching to Affliction I average ~14.5k DPS for single target fights (AoE in Affliction is not good right now). However, in AoE fights, with Destruction, I get more DPS than Affliction, but that's because Affliction is lacking in AoE DPS support. Again, after looking back over everything, I feel that Affliction is top damage out of all the specs right now, sadly. It's only my opinion, but I much prefer Destruction because I like to rain down the AoE fiery doom, but with Affliction I have to stick to one single target to get good damage. And, yes, overall Affliction has the better DPS/Overall damage it seems. Just keep in m ind that I have nothing to back this up as I never parse or log in the log sites simply because I'm not in Mythic gear and content. But, this is just my own personal observations from playing all three specs.