I’m a little dubious about any tip that advises: “It’s also worth noting that this fix doesn't always work on the first try. In a recent update it took me two tries, but some users have reported it working the first time, while others have said it took many attempts.” This is generally a sign that you've stopped working with technology and have crossed into the territory of superstitious ritual.
The actual trick behind this invocation is to clear your Google Services Framework data. Once completed, your phone’s System Update page should show the last update as occurring in 1969, theoretically giving you priority for an update.
As a warning, this is an older trick (see How to Force OTA Update of Jelly Bean 4.1.1 on Samsung Galaxy S III without doing all the programmin... ), and I had used it in the past successfully. For the 4.3 update, doing this did still work, but after the update, I could not install anything from the Play Store. I think I had to remove and re-add my Google account on the phone to fix it.
I cannot say if this is true for 4.4 or not, but be forewarned!
I have done the steps both times for jelly bean & KITKAT TODAY everything is working its not rooted its the original update from SPRINT!! So i don't know where you went wrong...
I did that for the last update, but just waited for this one and got it OTA yesterday. My question is, what got updated? The settings all look the same, and the only differences I've noticed is that the notification bar is harder to read on the lock screen (lighter) and that I had to get a new file manager app to deal with Google's new sd card limitations. Is there anything useful that KitKat added on the S3?
For the s3? The main benefit is that it was designed to use less RAM.
Kit Kat has other benefits, but the main one is only available on nexus devices for now