From what I understand about black ops 2 split screen mode is it can do the same 2 player split screen as 360/PS3 with both players on the main tv or it can split the image so one half is upscaled to fill the whole tv screen and the other half is sent to the gamepad. It's no different processing wise to what the ps3 and 360 are doing with their split screen mode. It's making use of the wii u's built in hardware upscaler.
Lets not forget that the wii u version of black ops 2 has a marginally inferior frame rate to ps3 and is a lot worse than 360.
https://www.youtube.com/watch?v=doMx1UEKEzU
The idea that the wii u has the power to generate 2 full action screens when it can't even keep up in single player makes no sense. Especially when there is also some missing detail in the graphics of Black ops 2 on wii u compared to 360 and PS3. All have a native resolution of 880x720 which is pretty dire anyway.
Adding the resolution of the gamepad to the main screen resolution makes absolutely no sense most of the time. However I believe the gamepad can create a full independent action screen but this would be using the wii gpu that is embedded in the main gpu and would have more limited graphics dictated by that gpu's limitations. Also this would have a massive hit on cpu resources.
The key to the wii u design is a high speed compression section in the gpu which at any time can downscale and compress the main gpu frame buffer or compress the wii frame buffer and send it to the gamepad. The wii gpu performance level is 12 gflops (gamecube was 8 gflops), the wii u gpu is 176 gflops. So you can see the huge difference in performance level. Even if you add that 12 gflops to 176 gflops it's only 188 gflops. Still a huge difference to the 1.3 terraflops of the xbox one or 1.8 terraflops of the ps4 gpu's.
