I'd recommend against using cleaners on the screen. I'd use that and a micro-fiber cloth on my iPad 1 and it ended up with all kinds of small scratches from the dust that would accumulate in the micro-fiber cloth. I don't know if the coating wore down due to the cleaners, but I suspect that is what happened. These products were labeled as "safe" for all screens, including specifically the iPad.
I'd recommend using water only, and perhaps a micro-fiber cloth, or just use paper towel with water. That's what I've done on my iPhone 4 and it stays very clean and without scratched. The coating still seems impeccable on the iPhone.