I had the same issue with typing on the s3. Everyone talks about how good it is, but I actually was looking for a keyboard exactly like the iPhone one. Maybe I have just used it so long, but I just type away and rely on autocorrect.
The iPhone's keyboard is just more accurate and the touch response is precise for sure. I was at the store this morning and had a whole bunch of clothing in my arm at the cashier and could type 1 handed just fine with the iPhone. The Note 2 was impossible to type 1 handed even with the 1 handed keyboard enabled.
Ha, i hated typing on the iPhone. Swiftkey is sooo much better. Hec any Android keyboard ive tried is better. Swiftkey Flow is just awesome. Its got all the features of Swiftkey plus the features of Swype. Damn good keyboard. There are other good ones too. I find it hard to believe you cant find one better than the crappy iPhone keyboard.
Give Swiftkey flow a shot
SwiftKey keyboards look ghastly and it doesn't solve the touch response issue. Not to mention there isn't even a 1 handed option.