The biggest problem for Microsoft's Xbox One (back at launch) was Sony's last minute decision to change their hardware on the PS4. They really pulled that out the bag and surprised even the developers. To be able to up the spec with more / faster RAM and a beefier GPU at pretty much the last minute was a bold move that paid off.
I really don't think the hardware is the biggest factor, and it's also why I'm not convinced trying to out-power Sony is the answer to their problems. The majority of console gamers buy consoles because you buy them and they work, they don't get involved in PC because they can't be arsed with the hoo-ha - these people aren't interested in how floppy the console is etc.
There are two main reasons the PS4 out sold the Xbone, that then lead into a third reason that is hard to overcome...
The first two things were price and games selection (both at the time and in future) - Sony were able to piggyback off having exclusivity with Naughty Dog and therefore Uncharted and TLoU, along with deals with Bungie for Destiny, Activision for CoD etc, meanwhile the only exclusives MS seemed to be offering were more sequels in already tired series like Halo and GoW, plus at launch the PS4 was seen as the console offering the "indie experience" and supporting indie devs. The second thing was price, because MS forced you to buy the Kinnect with the Xbone, you could get a PS4 for £100 cheaper at launch, this made a HUGE difference.
These things, mainly the price, led into the third thing, people will buy the console that most of their friends have so they can play with them, and because the PS4 got out of the blocks much quicker, its player base grew exponentially, as it was the one for most people that their friends had, so it's the one they bought.
The early adopters and non-casuals will jump on the console with the highest performance, but eventually it comes down to what games can I play and who can I play them with.
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