Destiny saves can be transferred from old-generation consoles to new ones

How Destiny Handles Cross-Generation Save Transfers

Bungie is "really interested" in allowing players to transfer their Destiny characters between PlayStation 3 and PlayStation 4, and Xbox 360 and Xbox One.

Tyson Green of Bungie tells IGN this is "because there’s going to be a lot of people who buy Destiny on a PS3 or Xbox 360 and then they get a PS4 or Xbox One for Christmas. Then it’s like, ‘Don’t tell me just wasted my last four hours there.’ So we’re really interested in supporting that."

The Destiny team doesn't "want to lock people in," so it seems likely your save data and characters will transfer between generations.