MMMMMMMMMM.............I play on a 52" tv-non-flat screen and my girlfriend plays on a 38" flat screen (vizio) right beside me and between the 2 tv`s when I looked at her screen, I wasnt moving when I actual moved. I was almost a half second off. Since then I assume that we all are alittle off when we move. So, thats why when we run around a corner while being shot at and we get killed around the corner, we probably arent really around the corner on the persons screen thats actually shooting at us but we are on our screen. So when we shoot I guess we dont really shoot when we think we are. Welcome to lag I guess.
I know for fact, everytime you switch to a different tv, you have to change your settings for your controller. Like I said, I play on a 52" and when I go to my girlfriends house, I play on her tv and my settings are way off. I tried to play on my 38" flatscreen and it was very hard for me to get my settings close to what they were on my 52".
I have no real answer about the cables but personally, I dont think it matters awhole lot about that.
The only thing you can do without buying a new TV is go through the TV settings and change the viewing mode to "Game" if it has it. Oh and make sure in your Wii settings you have it set to 480p.
Are you playing MW3 on your Wii U? If you're not, then you can't hook up your Wii with a HDMI cable.