The Game Rewind video is much, much better and lets me see the footwork more than the youtube video.
For future reference: the Amendola play occurs at 3:25 in Q4 of the Patriots-Jets, week 16, 2014. The Edelman play occurs, of course, at 2:06 in Q4 of the Super Bowl.
I've looked at the Amendola and Edelman plays several times in slow motion on Game Rewind. Unfortunately, I don't quite know how to post that here. But anyway, some differences:
(1) Edelman pivot is quicker than Amendola's.
(2) Amendola seems to use mainly his right foot to do the pivot. He kind of swings his body and left foot around both before and after the right foot has been planted. The Amendola pivot is a much more prolonged and fluid process than the Edelman pivot.
(3) By contrast, Edelman seems to plant both feet, then use both feet to pivot, while keeping his body and feet aligned.
(4) possibly Edelman is crouching more, not sure.
(5) The Amendola play looks "normal" (I mean, for a top NFL receiver!) somehow. Edelman seems to almost break the laws of physics. Pivotgate?