I would say look at what games are available for them in terms of exclusives and such and pick which one interests you most. Because ultimately this is what I did in the end neither of them had backwards compatabilty when I got my XB1. I had been with PS since the PS1 days and seeing as PS4 wasn't backwards compatible and the fact that I was interested in playing the Halo games I chose the XB1. Of course since then they've had some baqckwards compatibility added XB1 can now play some 360 games and more are being added all the time and PS4 is having PS2 games added to its library. If I had this info now that I had then I'd probably still would go with the XB1. But again that's more down to the games
Definitely not a decision to make lightly. Check what multiple videogaming sources say, look up personal experiences and objective statistics about the consoles. A friend of mine has an X1 and I have a PS4 so these are my thoughts on the dilemma:
1. PS4's interface is, in my opinion, quite a lot better than X1's. More intuitive, more pleasurable to use, sleeker.
2. PS4 is a more "powerful" machine technically speaking. I'm not entirely sure what that means but there have been numerous independent tests done on the two to confirm that. There's not much in it, but PS4 has better visual fidelity and "smoothness of gameplay" (I study Medicine at university, not English)
3. On that note, In NON-EXCLUSIVES, PS4 runs better, sometimes at 1080p while the X1 is going at 720p. Is that important? can you tell the difference? Who knows, but there it is.
4. I prefer the PS4 controller, it's lighter and less of a burden on my dainty fingers, but that's just pedantic. The Triggers are very sensitive on PS4.
5. I've found that, in times of sale, the PS Store is better value than Xbox Live Marketplace and even, sometimes, the evil empire of Amazon itself.
As sjsharp says above, exclusive games can be key to which console you buy. Since I only play scum RPGs, which are released on both consoles, this isn't a problem for me, thank goodness. Also, to reiterate again the good points of sjsharp, X1 does have quite a good emulation-based, easy-to-use backwards compatibility service. But, a. you might already have the old console, b. it doesn't work on every game (their catalogue is expanding rapidly over time, and user-submission is being accepted currently!) c. Playstation Now is a £12.99 a month service (with free 7 day trial) that allows you to STREAM a broad catalogue of PS3 games on PS4, which isn't too bad of a deal considering the amount of play hours you could get out of that.
In conclusion, both are great pieces of tech that are less expensive now, and that's always good. If you have the knowledge, the money, and the time, though, a great Gaming PC is probably a better investment.