Mail push does not work

I know this is already being talked about in other threads, but I can't seem to get a clear answer that each thread agrees on. Put simply, my Gmail does not push to my iPhone4. I used to have an iTouch and it pushed just fine there, the only difference between the two devices is that on the iPhone4 I set up the Gmail account under the "gmail" account type, and on the iTouch I had set it up as Exchange. I've read that this alone will make the difference, but it was an old post and I wanted to confirm. I've also read that som emails (Gmail included) simply do not push, but as I said it seemed to push on my iTouch so I wanted to confirm.

I have all the settings in the phone set to recieve push so I can get mail as it is sent to me.