As others mentioned, weve already had examples of dual-screen gaming with the Sony stuff. Even if it were an issue in the manner you described, a simple client download to the handheld, included with the main game, from the home console would fix that pretty easily.
This was one of the first things I thought of when I finally grasped the Wii U approach; Sony's Remote Play stuff is fairly mature and it performs pretty well on a WiFi network. The Vita has pretty much every sensor and input method that the Wii U tablet controller does. Could make for some very interesting new directions for games.
I mean... I can't take credit for this, but...
... you can't help but notice this.
Anyways, point I wanted to make is, on a technical level, these two setups are remarkable similar. Do we know the rez/spec of the tablet screen on the U controller yet?
(edit - I want to add, this is a good thing for both, they reinforce each other, no one should be unhappy about this if you are a fan of either)