You can see the comparisons on the visuals from the PS3 and PS4 for the Beta test of Destiny.
The guys at DigitalFoundry took some footage during the Beta from both the PlayStation 3 and PlayStation 4, so far you can see that the PS3 can still provide great visuals for Destiny, though a bit blurry compared to the next gen PS4. When looking at the PS4 footage, there are some effects that are only visible to the next-gen console, such as those flare effects when characters teleporting to the scene. Despite lesser effects, the PS3 version still packs a good punch.
Next on the video is the framerate comparison between the two consoles for the game. Both games run at 30 frames per second, what’s really impressive is that the PS3 version can still run the game at 30 frames though there are rare cases that it drops the FPS at around 28 as its lowest, while the PS4 can maintain a 30 framerate from the video test.
It seems like PS3 users can still enjoy the game without sacrificing much detail on the visuals, but they can still use their PS3 save datas once they transitioned to the PS4 as Destiny allows save transfer from last-gen (PS3) to current-gen (PS4)
Destiny will have its retail launch for both the PlayStation 3 and PlayStation 4 on September 9.