Well, I think the out of box experience (for the Day One edition, at least) is superior to the PS4, but they're both very slick consoles. On the Xbone, the software update went very fast and very smoothly, although things might be different tonight and tomorrow when all the other Day One buyers hit those servers. It appears to me that MS truly applied their 360 experiences, even on the very small level, and improved the Xbone. Little things like the login, and the controller connection, and so on, are just more polished and more convenient.
I did hit one glitch when trying to setup network access. Initially, I just transferred the cable from a 360 to the Xbone etnernet. It started the update download and then I accidentally interrupted it while setting up the PS4. Then I had a tough time getting the Xbone back online. I finally swapped out to another Ethernet cable (although the first one had been working fine) and the Xbone liked that one. Following that brief frustration, the Xbox One performed valiantly for several hours straight.
Although my wife didn't allow me any gaming time on the Xbox One today (which was fine. It's her Christmas present...), my kneejerk impression is that the Xbox feels a bit more innovative than the PS4, but that's an extremely shallow first impression. Overall, though, I'm glad that I chose NOT to choose this generation and popped for both boxes during Week One.