Personally I believe the game (Destiny) was meant to be enjoyed on the PlayStation 4, with its amazing graphics and superior quality, but that's just me. I have both next-gen consoles and I've noticed that the XBOX ONE makes a loud nice during boot up, probably because it has to work harder to render, not to mention the larger fan.
TL;DR
PS4 has better graphics, capped at 60 fps
Obvious choice for Bungie. Only machine capable of rendering such an amazing game
Edit 1: Thanks for the response guys. Obvious conclusion is that this game was meant to run on the SUPERIOR console: PS4- XBOX truly is weaker
Edit 2: XBONERS getting really mad. Hey, the stats don't lie!
Edit 3: From what I've been hearing, the situation goes like this:
XBOX ONE: 720p capped at 30 fps
PS4: 1080p native at 60 fps
PS3: 640p upscale to 720 30 fps
XBOX 360: 480 upscale to 720 30 fps
PS4 seems like the way to go so far until proven otherwise
Edit 4: receiving massive backlash from the community. What they don't understand is that Bungie purposefully said that it's at 30 fps across all platforms so the XBOX players would not be offended. The game was designed and built to take advantage of PS4 hardware, therefore it is capable of running at 60 fps solely on the aforementioned console.
Edit 5: Very heated debate I see. Questions coming from both sides. The thing is that Bungie did not want for one side to be left in the dust, so they just told everyone that it would be capped at 30 fps when it actually wasn't. 60 FPS PS4 confirmed. Check when booting up next time. You'll notice a small ticker
Edit 6: PS4 specs that suggest it can run, and does, Destiny at 60 FPS 1080p Native
CPU
Number of Cores/Threads: 8/8
Frequency: speculated to be running a base clock speed of 1.6 Ghz on a 2.75 Ghz capable chip
Shared L2 Cache: 2 x 2 MB
Manufacturing Process: 28 nm
Custom CPU for background processing such as downloading and recording gameplay.
GPU: AMD next-generation Radeon based graphics engine
Edit 7: this debate is getting very intense. Some players have even decided to bash the PlayStation community. I don't see why they would do that because this is ABOUT GRAPHICS COMPARISON and not some place for your complaints.
Edit 8: I've been receiving some very hateful messages, and yeah I get your frustration. The backlash has been tremendous but I've tried my best to clarify the situation; User xx_n1gg4bLazE_xx made it very clear to me that the community is unwilling to listen.
The point is; BUY BOTH CONSOLES-SEE FOR YOURSELF
Edit 9: finally some users have reported the difference between the two. Unfortunately YouTubers trying to upload video with a comparison, are limited to a 30fps cap, rendering the defense useless.
Edit 10: (UPDATE)- Thought this thread had died, but the community is still up for a healthy discussion. Receiving backlash from the community, don't know why, as for the 60fps cap on YouTube yes it has been raised, video however, will be difficult to see as it won't be the same as seeing it directly from the console itself. Graphics wise the two consoles are I guess on-par, with the limitation that PS4 renders Destiny at 60fps.
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I seriously doubt the human eye can tell the difference between 30 and 60 fps without being told there was a difference beforehand.