Nintendo's weaker console, attached Gamepad which people most people don't see the appeal of, poor marketing / naming and weak launch lineup basically made it a non-issue in the competition with the PS4.
Microsoft aggressively pursued the digital, DRM, always online and Kinect stuff with the Xbox One announcement, and recieved big backlash for it. My guess is Sony would have been happy enough to go that way (minus Kinect) as well if gamers had looked like they would accept it at this point, but they didn't, so really all Sony had to do was show off the PS4 and keep their mouth shut about all that other stuff. Thus a meme was born: PS4 >> Xbone. It didn't really matter that Microsoft later backtracked on some of the digital only and always online stuff, the damage was done. And when the story at launch was that the PS4 could perhaps pack in a couple more pixels for 100$ less, while the more expensive Xbox got you a Kinect, both consoles were pretty successful but the launch sales rightfully went the way of the PS4.
After that, the PS4 had the memetic superiority from the initial announcement and more momentum, more friend power from higher launch sales, and those things snowball to keep giving higher sales. Xbox One eventually made itself more competitive by unbundling Kinect to lower the price, providing really cheap bundles for the holiday and arguably a slightly better exclusive lineup (PS4 really didn't set itself apart from the other consoles with its exclusive this year), but the PS4 was already well ahead in sales and word of mouth. And while I think the narrative is somewhat true that the PS4 won this year by a mile despite not really doing anything better in terms of game lineup, it looks like next year it has a great year for exclusives (though I'm personally not really interested in any of them), allowing it to continue its dominance.
The pool of informed gamers looking at all the consoles might have the majority prefer the PS4, but I think that it's among less informed people that the preference for it is even higher. All it takes is a few buzzwords and scraps of info to get out there and then perhaps be exaggerated and the Xbox One (and even more so the Wii U) are dead in the water compared to the PS4. I think so many people's thoughts on why the PS4 is better go back to that initial announcement hype and the fact that on power / graphics comparisons, the PS4 bars go a little bit higher on the bar chart (and the Wii U's bars, if it even makes the chart, barely register). It doesn't matter that much that a lot of the differences or disadvantages from the Xbox One announcement no longer hold true, or that the graphical disparity is not that great (or that the "not troo next gen" Wii U has the best recieved exclusives at this point). The perception is out there in the mainstream, and it allowed the PS4 to kill the competition even before it got out its big exclusive games.







