Well, you could think of the PS4 and the PC as distant cousins, quite true. That would make the X1 the PS4's slightly more stupid half-brother, though.
AMD's laptop oriented Jaguar APU, a combined CPU/GPU solution, is serving as the core for both systems. The primary differences in terms of hardware are faster RAM in the PS4, slightly higher clock rates for the PS4's APU and the X1 reserving some of its processing power for Kinect. They're still very similar, although the PS4 is more capable. The difference isn't exactly big, especially if you're comparing the difference between the PS4 and the X1 to the difference between the PS4 and a decent midrange PC.
That's why I'm fairly certain developers won't put much effort into specifically creating games that exploit the PS4's advantages. Making multi platform titles look better on the PS4 is going to require more work; whether it's because the X1 version is polished or further until it suits the PS4 or the PS4 version getting downgraded until it runs well on the X1, it's all extra effort that I don't see developers pouring into their games. Not for the small difference it's gonna make compared to a hypothetical PC version, for example.
There might be some games that will look better on the PS4, but I'm willing to bet that the differences are hardly going to get noticed outside of some in-depth tech analysis - which most people won't do. Sure, there's bragging rights (YouTube comment section is always crawling with people to whom that seems important, for example), but if you're that interested in graphics for those rather small difference to matter to you, you'd be spending the ~400 bucks on a GTX980, not a console, either way.
What I'm trying to say is, don't fall for the people who'll tell you that the PS4 is two billion times more powerful than the X1 (and there are some folks on here who would, going by the PS4 / 4K gaming threats), because that's not quite true. Hence why I'd be basing my decision on the software, mostly. Granted, my point of view is somewhat skewed because I already own a gaming PC that's holding up well enough to run console ports with higher graphic settings than the consoles can; I don't know whether not having that options would change things for someone else, but you might want to take my opinion with a pinch of salt, anyway.
All said, I'm currently favouring the PS4 slightly, but my final decision will be based on what FM6 and GT7 will be like. Might be I won't bite at all if neither turns out to be a significant improvement over their predecessors (which would be a damn shame, really).
/edit:
Sorry for rambling on like that, by the way. Got carried away a little