The consoles have a market a lot of PC games, MMOs and mobas aside, just don't get. That's just the nature of a gaming platform that is designed to also operate as a home theater system and has the convenience of pushing one button to operate and being being in the middle of one's home. People buy a console for two things: convenience and community; the latter ironically is largely perpetuated by the former.
Why an Xbox One?
You have games like Halo and Gears of War, which just aren't on the PS4 and (for a very long time after release) PC. The Xbox has statistically more players than the PlayStation in the US, period, so the games are a little more lively (but not noticeably unless it's an old game). The controllers are oh my God, I can't even begin to start on how comfortable compared to the anorexic mess of a PS controller, which to be fair, they improved a little since the PS3. It can do everything, from Verizon television to Amazon to Netflix to Skype, browse the internet, watch and upload streams and has a pretty simple, straightforward UI. Xbox Live's security is a decent deal stronger than PSN's, but it's Microsoft, the king of the computer industry.
Why a PlayStation 4?
There are certain niche markets on the PS4 which is primarily why people buy it. A lot of the RPG games are great, as they have all the Japanese-based ones. They had great F2P games as well, like Planetside, Dust and Ace Combat Infinity (they should have released Infinity on the PC as well but they're idiots, could have made so much money). The graphics are and always have been astounding, though with the current generation the differences are hardly noticeable. Can also do Netflix and all that stuff (not sure about Verizon and Twitch though).
Pretty much every core thing a PS4 can do, an XB1 can do, and vice verse. They both have the F2P games, they can both play Netflix and all those apps, they both play the same games the same way, their GUIs are both good in their own rights and both have backwards compatibility; Xbox is just getting it late because they wanted to rush it out the door on launch, so starting this month. I mean, pretty much, they're the same minus label and a few nuances. The differences the 360 and PS3 had were far greater than the differences this gen has.
So if you're going to buy one, ignore the fanboyisms of both and buy the one that's most comfortable to you. Which one has the more comfortable controller? Which one has the cleanest, easy to use GUI? Which one has the online features you will use more? What (if any) exclusive titles would you want to play most? These are the questions you have to ask yourself after giving both a run. It really comes down to preference.
I like the XB1 because the controller is a perfect fit and the GUI is virtually identical to (insert Windows product of choice here). That's about it. Every game I've bought on it, I can buy on the PS4, and almost every app can be downloaded.