My heist comparison between the two.
Controller
The DS4 is a HUGE improvement over the DS3. The thumb sticks are better sized, the triggers are a great design and the overall size is nice. However I'm finding I'm continually getting cramp in my hands, only on the PS4. The battery life seems pretty poor, typically I'm charging every 3 days (around 8hrs use).
The One controller has some subtle improvements over the 360, but if there's one change I don't like, it's the LB/RB buttons. They feel too high, and sometimes difficult to fully press. The battery life is incredible (25hrs I've managed), which can easily last me 2 weeks.
Dashboard/OS
The PS4 looks clean, slick and easy to navigate. Switching between the dash and a game is faultless.
The One on the other hand looks like W8, not necessarily a bad thing, and offers some great apps (I've used Skype a few times, and I'm impressed). The OS is intuitive and looks far nicer than the PS4, for an overall experience.
Graphics
Both are stunning. But on identical games, the PS4 is very slightly better, although not by as much as 720/1080p IMO.
I've experienced no dropped frames on either, no stuttering and no tearing.
Sound
I use optical out to my amp for both, and the fact the One doesn't have DD annoys me. I expect this to be updated though.
Blurray
I've watched A Christmas Carroll on both. I couldn't see any noticeable difference between them.
Reliability
Neither console has caused me a problem, apart from the PS4 booting into safe mode after the latest update, and taking 45 mins before I could finally use it again. They are both whisper quiet.
Recording/Streaming
I've tried both. Obviously at present only the PS4 offers Ustream and Twitch streaming, but it's a great feature. I've used it a few times with friends (who don't have a PS4).
The recording feature is similar on both. Double tap the share button on the PS4, or "Xbox record that" on the One, and you've saved the last ~5mins.
Editing is better on the One, but both lack features I'd like to see added (upload to Youtube).
Games
Both have a pretty poor 'next gen' line up barring a few (Forza, Killzone, Ryse).
Which one?
Which would I choose if I had to sell the other? I'd keep the One and sell the PS4.
I don't plan on selling either, as eventually there will be exclusives I want on both.