The tl;dr answer for me is 'it's all about the games!', but there's a little more nuance than that, obviously.
10-15 years ago, a much larger percentage of the games on a console were exclusive to one system - yes, there were lots of multiplats, but there were also lots of games unique to a particular system. These days (well, starting in the previous generation, but even more so now), the vast majority of the titles coming out on the consoles are multiplats. The cost of development has risen high enough (and the systems have become related enough, hardware-wise) to make multiplats the rule, not the exception. As a result, when 90% of the games on a console are going to be available on all consoles, the only way to convince someone to buy more than one console is to have exclusives that make the console worth the price of admission.
In my case, I've already bought a PS4, and barring some magical software changes, I expect to buy every multiplat on PS4, regardless of how many systems I eventually own. Why play on relatively underpowered hardware if given the choice? However, if the Xbox One manages to snag enough exclusives that make me want to buy the system, I'll buy it. For example, I've never actually played a Halo game. Ever. But the Halo Collection coming out this fall is almost enough by itself to make me consider getting an Xbox One. I know that if I want to play those remakes that the Xbox One is the only place where I can. Same with games like Quantum Break, Forza or (yes, even) Tomb Raider. I might not care about each of those games individually as much as I do Halo (or something exclusive on PS4 like Driveclub), but given a large enough body of interesting games I can't get elsewhere, I can be motivated to buy the console.
In my case, system cost isn't (directly) an issue. I picked the PS4 over Xbox One initially because it provided more powerful hardware for lower cost, but I'm willing to pay Microsoft's current asking price if the games are compelling - hell, I would have paid the old price, and unlike many, I actually *like* the idea of Kinect, even if it's not being used to the extent it could be. I'm not looking for any apologies from Microsoft, though I could certainly use a little bit less of their astroturfing campaign. If Microsoft can promise me anything that would affect my decision of when to buy, it would be that they're working to bring more compelling, exclusive games to the system. (That, and to never EVER think about implementing any of the phone home/DRM stuff that got them into trouble when they first announced the console.)
