The Destiny beta has yet to hit Microsoft's consoles, but video footage of the game running at 1080p on Xbox One has been released.
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The beta on Xbox One will only run in 900p, but the full game's resolution will be 1080p on launch. The video of that 1080p footage is below, courtesy of IGN.
Destiny looks very nice on PlayStation 4, and not much less attractive on PS3--Bungie has done a good job of keeping the versions similar despite some extra bells and whistles on the current generation version. The PS4 and Xbox One editions of the title could likely look even better if not for the necessity of straddling two console generations, but Destiny is not--and won't be for a while--the only game dealing with this issue right now.
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Sports games in particular have to deal with this dilemma, as the yearly iterations don't justify leaping fully onto the new generation of consoles while most of the fans still own only a PS3 or Xbox 360.
Still, most games on the new hardware do look noticeably better compared to their last generation counterparts (NBA 2K14 is a great example). And while it would be great if games only featured improved graphics made possible by the new hardware, this two generation system will likely continue for at least another year or two--possibly longer.
There need to be enough current generation console owners for publishers to abandon last generation's huge install base, and that will--unavoidably--take time. This doesn't mean you'll be getting unattractive games until that times comes however, as you can see in the vide below and in plenty of PS4 and Xbox One title so far.