While most games aren't running at 1920x1080, or 1080p on the Xbox One, the upcoming shooter from Bungie, the studio behind Halo, will be running at 1080p on the Xbox One.
As you can see in the above video, this is what we should expect from Destiny on the Xbox One. The beta that is available right now isn't running at Full HD, but rather 900p. The final version of Destiny on the Xbox One has been confirmed at 1080p. Destiny isn't far away, as it'll arrive on September 9, just a couple of more weeks away.