You don't see anything on the controller screen while you're playing on the TV screen. If, for whatever reason, you had to let someone else use the TV, you could switch to using the screen on the controller, so the other person could do what they wanted.
Anyway, being a Nintendo fan since I was a little kid I'm probably gonna end up getting a Wii U. It'll serve as a good replacement for my barely-working Wii, too.