The most glaring impression is the size of the machine. It could easily be a doppelgänger for an early 80s VCR. This thing is massive. The only game console I can recall matching—and maybe exceeding—the overall dimensions is the first PS3 with its big domed cover. I'm fairly certain the Xbox One could be a foundation brick for a large building. Without getting out a tape measure, it's easily two-plus inches wider and deeper than the PS4. I have no idea why it's so massive. I'm going to speculate the size might have something to do with heat. And if that's true I wonder what will happen with the Xbox One S with the power supply inside the case.
When comparing it to the PS4, the Xbox operation seems to be more complicated, but it is a Microsoft product so that's easily explained away. And PlayStation Plus is the clear winner over Xbox Live Gold. PlayStation is also the winner in the setup procedures. I had to hard reset my Xbox One three times before it would recognize the fancy Dusk Shadow controller. And let's not mention Xbox isn't using Bluetooth for its controllers. Major strike against it. With PlayStation controller syncing just turn on the machine with the controller attached to charging cable and you're off and running. As for controller feel, I don't have enough time with Xbox to make a good comparison.
The last impression for now is network. The Xbox One is a bandwidth hog. I simply can't do anything else while it's downloading. With the PS4 I'm free to do other Internet stuff.
Okay one more thing. Backwards compatibility. This is something PlayStation has done in the past and I loved the fact it was compatible with previous generation games. Now it's all but nonexistent. The Xbox people are making games backward compatible. A major plus for Microsoft.
I will have a follow up post once I get more time with the Xbox.