Do you have the US version or international version? I have the international quad core version which is noticeably faster and has a vastly superior GPU, so if you have the US version yours may not be as smooth as mine. I make my comparisons to my iPad 2 because I don't have a 4S and never have. S3 is smoother than my iPad 2. It loads everything more quickly.
There's loads of things you can do on the S3 that you can't do on the 4S, how many do you want me to list?
- use widgets on home screens.
- swipe away individual notifications you're done with.
- toggle settings like wifi, Bluetooth, screen brightness, etc quickly using the notification bar (or home screen widgets).
- use any app that relies on NFC.
- run any app in the background including ones that need to maintain a constant connection, for example IRC clients. This also means you can have something like Spotify start downloading a playlist and just leave it alone. On ios it would stop after ten minutes; on Android, it doesn't.
- access the file system.
- DLNA.
- send any attachment (and multiple) directly from an email composition screen.
- gallery shows photos from PC using DLNA and also online sources like Picasa.
- mount your phone as a drive on your pc.
- install custom keyboards.
- use live wallpapers.
- install apps from outside of the google play store.
- use custom home screen launchers.
- use custom lock screen apps, including ones that let you add widgets.
- take pictures whilst recording video.
- take pictures using your voice.
- answer calls using your voice.
- gestures such as flip the phone to silence it, put your palm on the screen to silence it, swipe across screen to take a screenshot etc.
- Bluetooth/wifi direct file transfers.
- thumbnails in the video player are live and show previews of the video.
- you can replace the default browser, messaging app, etc.
- built in maps has transit navigation, street view, indoor views of locations you look up, etc.
- download large apps on the mobile network.
- faster way of closing background apps and switching between apps.
- you can share photos directly from the gallery or other services to any service that implements the sharing API. For example, you can share Facebook photos to Twitter and vice versa. That's only an example, it can support any app eg. Instagram, Flickr, Picasa, etc.
Is that enough?