As a person who doesn't play console games at all, nor ever, I normally wouldn't have an opinion. However, last year I created the multi-player maps for the Call of Duty: Advanced Warfare Strategy Guide, published by Brady Games (now the company is Prima Brady Publishing). For research I played CoD:AW at Activision Video Game Studio in LA for 6 days in August, last year, while recording the video capture to my laptop. At Activision, I only had access to an XBox One machine, though the PS4s were half a room away - those weren't setup at the time for the developer version of the game, which was needed so I could run a level with nobody shooting at me, so I could spend my time studying the terrain of the level and details to get the map commission right.
While I don't really need to know how to play to make maps for their strategy guides, I considered the possibility of getting a console just to keep in practice play/recording it to be better at my craft (at least in that portion of design) - although, as stated, it isn't necessary. But I posed the question to the writers of the CoD:AW guide, who were with me at Activision, if I bought a console for my purposes, which should I buy. Unanimously answered by all the Brady Game writers (and these guys are addicts with the games in addition to writing for them) were PS4. They pointed out that for games like Bungi Destiny, there is a huge graphics speed and quality difference between the PS4 and XBoxOne versions of Destiny - in their words, the visual experience between the two are huge.
For most of the other issues brought up by Morrus, both are adequetely comparable, for the most part both PS4 and XBoxOne are the same in those respects. There seems to be a major difference in visual quality and frame rate, but only with games that use PS4's difference. Playing CoD:AW on either machine, because that games code hasn't been optimized for the PS4 visual enhancements, there is little visual difference between them, so no advantage for using PS4 with CoD.
Again, I'm no expert, but I did speak with experts on exactly this. Consider one of the strategy guide writers, the youngest one, Will Murray is like a 22 year old that has been playing video games on the competitive circuit since he was 16. Most of the other writers (4 altogether) are in their late 20's to later 30's, each with a decade or more of gaming and writing for those games. They all said, if I were to buy one console (at this time) its the PS4.
I've got no opinion on whether consoles are better than PC (though PC can't replicate the PS4 visual enhancements either), I don't play these games, at least not outside map commission work. On the first day of the visit to Activision, I did try playing CoD:AW for a couple levels for a few hours, and I didn't enjoy the experience. So technology games are definitely not my thing...