Have they mentioned whether or not a character would be cross-platform? I'm sure not, but that would be pretty cool.
Just that your character(s) is tied to your Bungie.net account, so in theory they could make them cross platform, but they have not said anything yet.
My guess is your character will be interchangeable between 360/Xbone or PS3/PS4 but not 360 / PS4 or PS3 / Xbone.