If you just go by graphics, more often than not the PS4 will win because it has better hardware and doesn't have the bloated OS constantly running as well. Benefits of a PS4 vs One come down to what you want in a gaming system and what exclusives you want.
I know PS4 should be better in most cases, but I guess it's partly a matter of how much better. Last gen, I remember seeing side-by-side comparisons of multi-plat games on PS3 vs. 360 where the 360 version clearly looked better (partly because the game was designed for that system and ported to the PS3). But then when I fired up the same game in my PS3, I thought it looked perfectly fine. TBH, I'm not really wanting to jump to next (current) gen for the slight graphics upgrade anyway. It's mostly because of the current gen "exclusives" like AC Unity and the nerfing of cross-gen titles for last gen consoles (Madden 15 and Shadow of Mordor). I just don't want a system that's hamstringed out of the box. Though at this point, I find the PS4 even more hamstringed due to missing features.
As far as games go, Sunset Overdrive and Fantasia definitely have my attention. I'm also a bit of an odd duck in that I like fitness games, and PS4 doesn't have any, even announced. While X1 has at least three I'm aware of.
I'd like to hear input from others with both systems, though this probably isn't the best thread for it. Maybe I should start a separate PS4 vs. X1 thread.