Galaxy SIII i9300 Jelly Bean/Touchwiz (Leak)
It is no secret that Samsung was working in the Jelly Bean update for it's flagship, and for a couple of weeks now, SamMobile.com has been posting leaks of the beta-test-soon-to-be-released firmware. You can flash the stock version of this firmware via Odin. It will not change your binary (flash) counter, meaning your phone will remain with it's official or stock status.
As it is no secret the Galaxy SIII stock with ICS is near or equally smooth as Jelly Bean in the Galaxy Nexus/Nexus 7, at least that's what I observed from using the Nexus 7 and owning a Galaxy SIII. But I'd say Project Butter is noticeable. Everything seems smoother, specially third party apps like the Facebook app.
Here are a couple of screen shots. Notice that I am using a Custom ROM based on the latest (not anymore) leak from September 5th. A new leak came out today, but I have not had the time to test it and the Custom ROM I am using (Omega ROM v20 by indie and Omega ROM team) is yet to be updated to this new version. Omega ROM is bloatware free if you choose so at the moment you flash it, but it keeps all features of Stock Samsung ROM, including the launcher (Omega ROM http://forum.xda-developers.com/showthread.php?t=1663656 ). Samsung is making changes to the settings menu at every new leak, they are likely looking for and ideal organization for the menus. I haven't noticed any bugs, so I am guessing that Samsung is very close to release an official update to all GT-i9300s.
Extended Notifications work just like in AOSP:
Google Now can be accessed from the Recent Apps menu, Google App in the drawer/homescreen, search bar widget and (at least in Omega ROM) by double tapping the Menu capacitive button.
You can see in the screenshots that the memory footprint has been greatly reduced. Now the device has 833mb of available RAM, against around 740mb in Ice Cream Sandwich.