Doubt it.
The game will still need to be able to run on PS4 and XB1. It'll probably be one or two years post launch before most console players will have switched over to the new machines.
Don't expect 60fps until "Destiny 3".
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I will be very upset if I get the next gen console and Destiny is not 60fps. If Destiny is 60fps I would be okay with cross-play with PC and console. And if they did that they would be bringing two communities together and make the Game grow even larger