I imagine there would be some kind of place that would showcase your achievements and that you would unlock certain things based on what you achieved in the first game. Or they would probably let you do certain things based on the weapons you had or even exotic you had etc. Guild Wars 2 did something similar, characters didn't carry over to the second game, but they had a "Hall of Monuments" that showcased your achievements from the first game. You were rewarded with some armor skins and other cool things to use on your new characters. I can see Destiny doing something like that, but I can't see them making us start brand new characters unless we really want to.