For me it boils down to the end experience. Xbox One (the third in the line I might add...) was created from it's beginning to be a set top box that plays games. Yes it's powerful, but it's core as an internet TV connector gets in the way of the gaming experience.
PS4 on the other hand was built for games first and secondly added support for online video streaming in a sandbox. This frees more of the CPU, GPU for actually, you know, playing games :-D.
Since they are nearly the same machine on the inside... I pick PS4.
Im no console gamer - the most recent console I've owned was Dreamcast - but if I had to choose I think I would go PS4. They seem to be aiming to please the gamer more than XBone who seems to be trying to do everything for everyone [its that whole Jack of all Trades, Master of None argument]. I also hear very good things about PS exclusives that interest me a lot more than XBone titles.
The Xbox One is more of a casual system compared to the PS4, The PS4 is easier for all out gaming where as the Xbox One is more or less for casual gaming in comparison. In my opinion the PS4 would be better for me as I prefer all our gaming, but alas I have a computer which is much better
In my opinion neither the choice should be Wii U. For these reasons.... I am primarily a PC gamer, my graphics card alone costs more then these systems....they are both mainly inmo want to be PC's.....and I'm not impressed. There is very little either offers I do not already have and I can even use their controllers with my pc.
However the WII U has things that are different. For one the Wii U gamepad is great if you are a father or mom who sometimes has to share time on the same machine. My gaming PC is hooked up to the big screen TV, so sometimes wifey will be watching a show, or my kid will be, but I can grab the gamepad, and get some game time in the jon, in bed, or where ever. Trust me when you are a parent you understand how cool that is. Also it works 10 times better then the Nvidia Shield with zero lag....I dunno how....but it does. Also it does offer a physical interactivity that other systems just really don't. Lastly the Wii titles tend to have the higher developer times on titles. seen the new upcoming Zelda game or the new Xenoblade Chronicles? They are absolutely mind blowing openworld games coming out this year! both look better then most of what has come out for PS4 or Xbox One..... You have to wonder how they are wasting their extra muscle with how good these looks on a console that they have claimed was inferior hardware wise. But these titles are proof what longer dev means in a final product. Also unlike most of the PS-xbox titles you know neither of those open world titles will ever come to PC. Wii U simply has console pluses that are different then what I already have on the PC, and it's accesable for anyone, and has more content for my kid.
I do have a Ps3 because it's an excellent streaming device for Amazon and netflix, but outside of that and to play blu-ray I never use it for gaming.