It's good to see multi tasking on consoles but i don't think it's valid anymore. Everybody has computer beside their console, phones even tablets. And all of them will be better to do other stuff than console.
I mean i have twitter facebook and all of apps i want in phone. Why would i use it on console ?
I think dedicated console is right way to go and there is nothing wrong with it if they would choose it.
Do you think either one wants to be the console that offers no functionality other than games?
Multi tasking isn't exclusive to things you can also do on your smartphone. On the Vita I can have a game running, look at my trophies, go to the store, go into party or friends, send a message, use flickr/twitter/facebook to upload a screenshot, change settings for the device, use the browser etc. All by pressing the PS button and switching seamlessly around the OS. One of the few limitations now is not being able to play a video while a game is running. I assume the Netflix app is the same, but it's not out here yet.
That is what the PS4/XB3 should be, and I'm sure are, aiming towards. The rest of your console will work almost entirely as normal while your game is suspended in the background. As opposed to the gimped way the PS3 handles it currently.
I see no reason how not having all the extra stuff could be considered a good idea by the people making the console. What benefit comes from only offering games? They save a bit of money on the team that makes and maintains the OS. On the other side they lose customers to the other console which offers full connectivity to the rest of the 21st century.
It's not about wanting to do it all, it's about having the choice and not being locked inside a box that when you want to do something trivial you have to break out of.
Also, I want to be able to send a video/webpage/photo from my phone or tablet TO my PS4 with a quick gesture. It shouldn't need the game to be shut down to do that, though I don't know about playing a video while having a game loaded.
Finding that funny youtbe video or that trailer might well be easier on your phone or tablet, but watching it is going to be better on your TV.