The update is coming over the air but may take some time to arrive at your smartphone doorstep so try to be patient.
The update brings the Galaxy S4 UI and many of its features, including Galaxy Gear support, TRIM (which significantly increases performance), the new Samsung keyboard, the new lockscreen, Adapt display screen mode, the Sound and Shot camera mode, move to SD feature, the Galaxy S4 S-Voice version and much more.
You can check out the complete changelog below courtesy of Sammobile and if you want to see a breakdown of the release by carrier can check out their tool for that under the Source link.
CHANGES AND IMPROVEMENTS IN ANDROID 4.3 UPDATE
How to update the Samsung Galaxy SIII LTE Version.
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The 4.3 I9305XXUENA1 doesn't have any problem with battery or applications!! it solved all my problems.