Wireless has a limited range for streaming. Besides if the Vita does practically the same thing and is not popular there is very little reason to think that the Wii U tablet feature will be more popular with even less capability.
Why? As the post above yours points out, most importantly, people will be buying WiiU for its games; something that Vita is not proving itself with at the moment. Vita is a completely separate purchase independent from the PS3. The WiiU is built around this philosophy and works out of the box. So developers can design around this principle as everyone will have access to its capabilities. So it'll be far more popular in this regard; it's not even close.
And the streaming is not just limited to playing a game on the gamepad instead of the TV; both screens can work in tandem with WiiU with one game. The Vita requires software on both devices - see Playstation All Stars - which means that the image being displayed on Vita while doing this is limited to its hardware. As we saw with the Zelda HD demo (running in real time) last year, WiiU can display the full game image on the TV and the gamepad simultaneously. Can PS3 + Vita (or Xbox360 + Smartglass) do that?
Yes in a sense.
That is some pretty cool interaction, but it further proves the point I'm making...
If you notice while LBP2 is being played on the "TV", the Vita is merely displaying simple shapes on it's screen; not the full game. Once Sackboy goes into the pipe and appears on the Vita, the action on the TV essentially stops while the Vita is displaying the full game. Also, I can't quite tell if the visual fidelity of the game on Vita at that point is the PS3 graphics or not (ala cross play games) but it may be.
With the Zelda HD demo on WiiU, you can see (starting at the 2:05 mark) that the full WiiU game image is being displayed on both the TV and the controller screen simultaneously. While this was merely a demo (and the image on the TV screen appears to be a bit smaller than full-screen during this), the graphics are running in real time, so I'm hopeful that this will be possible for future games on the console.
