Yeah but unless you are staring at your screen you will miss those notifications. Whereas with Android, you can see them as a notification icon at the top of your phone, or get a LED or vibration notification when you pick up/look at your device. The quote below answers some of your questions about what the S3 can do that your phone can't.
As for my personal experience, what I am finding that the S3 does that my iP4 or the new iPhone won't be able to, will be finding reading or surfing the web as pleasurable as with the S3. It is no longer a pain for me to do any reading or research using the S3. Oh, and although it's a Sammy feature, I am LOVING not having to touch my screen every 28 seconds to keep it from going dormant.
For others that say they miss photo stream etc. I rely on my iPhoto to save all of my photos. I have Automator import them directly to my iMac when both devices are on the same internet connection. Easy Peasy. It pulls the images into iPhoto through dropbox.
To sync contacts I just added gmail to my OSX mail version and set up the address book to sync with google.
The ONLY thing I am missing is that damn PvZ hasn't upgraded either for my device or my country. Not sure what their problem is!