Cheaper, more powerful, didn't fuck up marketing beyond one's wildest nightmares.

that. Plain and simple. The price of the Xbox One was the big issue for Microsoft and it was just too late for them when they reduced it, the domino effect of the Play Station Four price was unstoppable 

The PS3 also outsold the 360 most of the years the two were on market. The PS3 sold a ton of units overall, it just ate tons of money on the way to doing so, since Sony threw too much in there and made it too expensive to produce. 

Sony as a corporate entity catered to gamers with the PS4.

All the puns at E3, and all the Antonio Banderas PS4 Gif.

Building confidence in the brand thanks to their incredible efforts with the ps3.

As a ps1 owner, I was a happy customer. Some of my best years in gaming.
As a ps2 owner, I wasn't too happy. Took me a while to buy a ps3.
As a ps3 owner, I couldn't be happier. Beyond, The Last of Us and even GT6 showed that Sony will support their consoles even if they fuck up and at the end of the console's life.

I also bought a wii and wasn't by any means a happy customer. As such, I had no faith in wiiu. They didn't prove me wrong by the end of its support, so I'm glad I never bought one.

I also owned a psp and though Sony did a decent, but not great job with it, it was easily my favourite gaming device so I starved for a month and bought it day 1. I still don't regret it, though I do think Sony didn't try hard enough.

Don't know if that's the case with other people, but I assume a lot are unlikely to buy a console when the previous one left a bitter taste in their mouth.

Which entails forcing hardware on a consumer base along with underpowered hardware and relatively limited software support.  That's ALL it was.  Plain and simple.

MS killed all that goodwill gain during xb360 with the 2013 reveal.

The PS4 was the anti-PS3 showing they learned many lessons. It wasn't difficult architecture, it wasn't cutting edge, it wasn't expensive. It was a solid mid range console at a great entry price point with plenty of first and third party titles. Not only is it selling well, but it is very profitable along with PS+. I fully expect the PS5 to be an extension of the PS4.

I do agree the significance of the swing was aided by Microsoft making several poor decisions in the first year of the Xbox One and Nintendo's Wii U being a non factor.

Don't they always, the N64, Gamecube, the Xone and the original Xbox goofed hard. The Wii and Switch are wildcards since competition with PS consoles usually ends bad.