To clarify:
The Gameboy Advance Virtual Console menu allows you to have different screen modes. I will go over them:
Video Mode - Default
Default is beautiful pixelated classic Gameboy Advance goodness. The pixels are as square as they come, and at 1080p they're very well-detailed.
Video Mode - Smoothing
Smoothing adds what I could compare to a HQ4X(?) filter. Most pixels lose their square edges and instead blend without any fuzziness. There is no apparent slowdown (unlike some hq filters in emulators).
In addition to the video modes, you can change the resolution.
Resolution = Pixel-Perfect
Pixel-Perfect takes the original GBA resolution, and multiplies it until it's a number just short of the 1080p resolution used by the Wii-U. This means that the image you're seeing on the TV is the exact same ratio that the original GBA was. The drawback is that you will have a little letterboxing in your TV, depending on what kind of resolution your TV has (obviously if your TV's max resolution is, say, 480p like an older TV, or 720p like the cheaper HDTVs with the smaller sizes, your mileage may vary with regards to the letterboxing).
Example: you have a 1080p HDTV.
The original Gameboy Advance resolution was 256x160 (3:2 aspect ratio).
The Wii-U will calculate that it needs about 6x the GBA resolution in order to fill the screen (I am assuming right now that that's what it's doing).
So the game will have a resolution of 1536 x 960, and will letterbox the leftover 384 horizontal pixels on the left/right (192 on the left and 192 on the right) and 120 vertical pixels (60 on the top and 60 on the bottom).
As I play the game, this is what it appears to be happening, but I cannot confirm.
Resolution = Full Screen
Full Screen upscales the entire GBA resolution until it matches your TV's resolution, whether it's 1080p or anything else. The bonus for this is that your TV is completely filled with the content of the GBA screen. The drawback is that you're going to be playing on a slightly distorted image than the original GBA, taking advantage of those extra 384 horizontal pixels and those 120 vertical pixels, at the cost of a little distortion.
Distortion = the pixels aren't perfectly 'squared'. They may be a little taller or a little squattier than normal, depending on the TV resolution.