Base gameplay is nearly identical. Sprint, aim down sights, insta-kill melee knife. Now I know those are industry standards basically, but for a developer who actively ignored those elements for over a decade, to put them in, you know what they were doing. Of course Destiny has its own style with it's movement options, it's class differences and supers, and they've tried to have unique futuristic weapons.
And yes, Aim Down Sights is chasing Call of Duty, especially for Bungie and 343. Halo 5 is the clearest example of chasing CoD with aim down sights. Ham-fisting it into the game, vehemently trying to say it's about immersion, there is no penalty to it. It's something the fanbase didn't even want more than sprint, and yet moving forward it will probably be in every game until whatever else becomes the flavor of the month in shooters.