I'm not sure exactly what you mean. The phone supports Gmail natively. I just think the access to gmail features is limited, and the notifications do not sync. Same goes for facebook. I would get a facebook notification. It shows up on my facebook tile, and my "me" tile. If I use the app to clear the notification, it still shows up on the "me" tile. Kinda annoying. All the notifications seemed to work this way for me.
Example- when I use facebook for iOS, all of the crap (farmville) that I blocked from my computer do not appear in my feed. On the 920, everything showed up on my feed including apps and people I had blocked. And support for a lot of facebooks features are not there, much like gmail.
iOS certainly isn't perfect either, especially when it comes to notifications. Call me old fashioned, but I think iOS and WP8 would be a lot nicer if they used the status bar for notifications. All that vacant space just sitting there not being used. Instead we get annoying banners that I end up just turning off anyway, and app badges that you have to look for if the app is not on your first page. Why not use all that space to place different icons representing different notifications? This, NC settings, and lockinfo are the main reasons I jailbreak.