Here is my comparison:

Hardware:
PS4 is slimmer, sleeker, sexier, thinner, lighter, with power brick integrated
XB1 is clunky, bulky, heavy, with an external power brick

Controller:
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

Games
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.

Graphics performance
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.

General performance
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.

Internet capabilities
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.

Pricing
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.

It is appreciated that you tell people upfront that the comparison is subjective. Well, all comparisons are making more or less subjective, but this is to the extreme, you could've just put it as a Sony thread :). You will definitely enjoy your PS4, just as much as I will enjoy X1.

Hardware
I don't really care if its bigger or has a power brick since my console sits on the shelf. If I moved it a lot, then it would be an issue.

Controller
Kinect is a controller and that gives the X1 an edge.

Games
PS4 lacks Halo, so it does not have the edge.

Graphics Performence
PS4 certainly has the edge. I hope its used for more than higher resolutions.

Media Capabilities & Multi-tasking
X1 seems to have the edge at the moment. I felt it did last gen as well.

Internet capabilities
PSN is faster and more reliable? Hmmm... if you say so.

Pricing
PS4 has the edge.

Just a few quick notes...

Yes halo is under the Xbox umbrella, but the team (Bungie) who designed it is not producing Halo anymore. They are producing Destiny, which will be available in both consoles, and deemed to be the next Halo.

Yes, Xbox has Kinect but is barely used (almost certainly 99% of the games don't / won't use it) and hardcore gamers don't seem to care for it. Apart from the privacy concerns, all those "next-gen" Xbox features are actually "voice-controlled" not Kinect. Plus PS4 has already "motion" controlls in the regular controller while PSeye is up for sale if you choose to, still at a lower total cost

I am not saying PSN is better than XBL overall, all I am saying, the PSN performance on PS4 is much better than XBL on XB1 for now. This is specific to "now with next-gen consoles".

which point are you exactly objecting? Let's clear up the air..

Price => don't think so

Performance => don't think so

Hardware => don't think so

Controller => you may like the xb1 better (which I obviously stated there) but given that this is subjective, ps4 controller is obviously better with respect to its touch-pad, integrated battery, motion and speaker (that part is objective)

Internet => I have no conclusion about this SPECIFIC TIME AND MACHINES. Don't let your historical experience cloud your opinion.

Launch up games : I said XB1 is better

Future games : Given the subjective preferences and third party games aside, PS4 has far more exclusives, third party titles, indie titles, and non-western (japan etc) titles announced or planned (this part is objective). This makes it plethora of games larger, more diverse and more balanced...

Media capabilities : This is the most controversial one. Let's break it apart.

   I said ps4 does less => CORRECT.
   I said ps4 does those better => Also CORRECT

   I said XB1 promises more => CORRECT

   I said XB1 execution is problematic => CORRECT (voice recognition, snap mode etc)

  I said most of the XB1 functionality can be enabled with either PSeye, or native PS4 voice commands etc. Most of them are not exclusive to XB1. => Correct

  I finally said XB1 does more, PS4 does less but it is just better at it => CORRECT

I didn't take anything to extreme after all. I was just being open-minded, honest, and analytical... Whether or not you like it, is a different matter.

edited out the bullshit that my fingers typed

I can do one subjective comparision too.

PS4 VS Wii U

The Wii U, looks really cool. It comes in white and dark colors. I have the white one. The PS4 looks ugly.

The performance of the Wii U is really cool. I heard it can run games at 1080p and 60fps.

The internet services are better on PS4.

The Wii U is cheaper than the PS4 and Xbox One.

All around the Wii U seems to be a good console.

Sony was the first to have a successful console with aspirations of multimedia capabilities which is why MS joined gaming in the first place in bringing games into the OS. They just dont make multimedia a major priority. From what I've played moving through the UI is faster on the PS4. I havent checked the downloading though. Its also less confusing. MS needs to fix their compartmentalizing of Live. I like the Live aesthetic better though. The Kinect is also better than the Eyetoy, but if Sony adds the Move and runs with that with decent games behind it that could all change so MS has the edge there as well.The color coding helps where the lack of awareness of items are. The PS4 is still slicker and they found a very nice way of keeping the cross media around without being completely ugly. Its actually very nice. They will both get better with time. I agree with this, the only thing I can truly agree upon after playing both with MS winning out is the launch lineup. Hardware, functionality, controller and all so far go to Sony for me. The Twitch is also very smooth but MS should have more features on theirs later. Xbox Live is a constantly evolving thing, so it shouldnt really be an argument. I just hope Sony gets competitive in evolving the OS with Microsoft since Microsoft made that a big thing in gaming.

it doesn't?  Weird, I was watching blu rays, netflix, Hulu, and other multimedia functions on mine.  I mean, okay, we don't have Cable and Sports, but I've not had cable or satellite TV for years due to the internet and netflix, sooooo....yeah.  

Far as I'm concerned, Xbox doing multimedia is like Sony doing Betamax.  Great in theory, useless in practice. 

Halo 4 wasn't a bungie game and it was great. Destiny doesn't change Halo 5 being a potentially great game either.

Your arguments against Kinect aren't valid.
1) Most games probably won't use PS4's motion features either. But since Kinect comes with the console, there is more potential for developers to use it.
2) You feel Kinect isn't liked by hardcore gamers, but you didn't mention hardcore gamers while boasting about the PS4's motion features.
3) Voice control is part of the Kinect. Kinect encourages developers to use voice control features.
4) PSeye not being bundled means developers are less likely to use it.
5) Motion gaming on PS4 may not neccessarily be cheaper, especially if multiple people want to play. I believe the new Kinect tracks 4 people at once.