Here is my comparison:
PS4 is slimmer, sleeker, sexier, thinner, lighter, with power brick integrated
XB1 is clunky, bulky, heavy, with an external power brick
Both controllers are great, one may be better than the other with respect to personal preference
But ps4 takes the edge due to integrated rechargeable battery, integrated speaker & motion, and touchpad as well as the share button
XB1 has a better launch line up, but the upcoming games and history definitely gives the edge to PS4. For now, it's a slight edge but given that it's almost certain that PS4 will be a much better hit than PS3, just wait this gap to increase a lot more in PS4's direction.
PS4 is theoretically at least 40% faster though this can be as much as 2x. The performance gap in reality may change from zero in some third party games to as much as 2.25x; either way PS4 is well ahead.
So far, PS4 is far better; much faster installation times, faster Browser performance, faster UI, instant sharing, longer video recordings etc. There is not one area where PS4 doesn't exhibit higher performance.
Media Capabilities & Multi-tasking
Xbox is potentially better, but the execution is very problematic now. PS4 does everything promised and very fast at it, such as limited multi-tasking, smooth and fast game installs, responsive UI etc... XB1 promises a lot more, but the execution and reliability are poor. Multi-tasking is superior but having more than 2 or 3 apps open is barely a niche. Snap mode sounds promising but execution is horrible. Kinect might be appealing but all it is good for so far is the voice commands, which doesn't really need anything but speaker which PS4 has integrated in its controller! Plus most of this functionality can be enabled by PSeye camera and/or some software updates. In short PS4 does less, but does it much better than XB1.
This is correct if you are subscribed to online services. Otherwise, PS4 is outright better, while XB1 just cripples pretty much everything but single player gaming.
PSN is cheaper than XBL, has more bonus materials, and so far proved to be faster and more reliable. We'll see how it will turn out.
PS4 is better, period.
In short, my long run prediction:
PS4 will give a better hardware with better gaming and general performance and a more diverse, more balanced and much larger gaming library at a lower cost than XB1. The execution will be better although it will be a less capable machine than XB1, where it matters much less. It will do slightly less, but it will do it all much better.