Destiny will have different graphics for different platforms according to Harold Ryan, Bungie's president.
He didn't state what that meant between each platform, but it's obviously clear that the older generation consoles, the PlayStation 3 and the Xbox 360, will have worse graphics than newer generation Xbox One and PlayStation 4.
He didn't state whether there would be any difference between the PS4 and Xbox One, and instead said "We're not committing right now to any specific platform features. The great thing for us with timing is that we were making a new engine, and then two new consoles were coming out, which led us to invest more into making the new engine for it.
"There are a whole bunch of great opportunities for us to go after, like full player experiences, etc. We're investigating all of those and building the core experience of Destiny, which will be similar across all the platforms. The graphics are different, obviously, platform to platform, but in a connected world, the game of Destiny is going to be awesome on all of them."
So whilst there won't be any console exclusives, to really enjoy Destiny you may have to get hold of a newer console.