Go look then see for yourself.
Destiny runs at 1080p on both the PS4 and Xbox One, so we know that both systems are more than capable of running comfortably at 1080p. It isn't as if the PS4 outstrips the One in terms of visual potential, they just run on different architecture, so one is easier to develop for than the other. Not to mention that PS4 dev kits have been going out for years, as far back as at least 2011-2012.
The Xbox One and PS4 both have 8GB of VRAM, though the VRAM is different for each console, and each console keeps a different amount locked out for use in background systems (the PS4 gives developers around 4.5GB while the One gives around 5GB). Xboxes without a Kinect sensor can utilize roughly 10% more memory to dedicate to the GPU. The CPU in both systems is effectively the same, though the One's runs at 1.75 GHz compared to the PS4's 1.6GHz.
As far as graphics go, any cross-platform title for the One and PS4 will look 99.9999% the same, the other .0001% being that the PS4 is better at rendering things like foliage and small particles. The only way you're going to notice any difference at all between the two is if you look at a side-by-side comparison. And even then, only on an extreme close up of some grass. Textures and models look exactly the same.