Destiny is a game that spans console generations. The game comes out on September 9th, for the Xbox 360, PS3, PS4 and Xbox One, and with any multi-gen release, there are bound to be differences. Currently the beta is only available on the PS4 and PS3, so these are the two consoles to look at as far as doing a fair comparison.
The Destiny Beta runs at 1080p on the PS4, below you can see how the PS3 version shapes up to its big brother. It handles most things pretty well actually, however there are differences in shadow and texture qualities.
Check out the short video below to see for yourself, and remember to watch it in 1080p.