I just upgraded from 4.1.2 to 4.3 on my Note II, non-rooted on Three in the UK. Third day in, I haven't really noticed any benefits, but I do have issues with it:
1. First day after upgrade phone locked up after screen went to sleep, with general browser, email, pdf applications running. No response to nav key or power button. Had to remove battery as was unresponsive. Never happened before.
2. Second day after upgrade phone locked up after screen went to sleep with various standard apps and Ummano podcast app running. Audio still playing but no response to nav key or power button or volume key. Had to remove battery again to restart the phone.
3. Kindle app: volume button now changes two pages at once. It is virtually uncontrollable. It was fine when running 4.1.2. One press, one page. Now this functionality is rendered useless. Bad driver for volume key I guess.
4. Stock email background colour is now forced white. I hate that. I want it to be black again. Read email now looks like unread email as it is highlighted more. Bad design. Bad UX and no choice to change it.
5. Need more time to enter lock pattern. Screen goes dark again in about 5 seconds. Cannot find any setting to adjust this. Annoying.
6. Generally 4.3 ignored a lot of my personalised settings and is behaving as though I am a new user, running first-run screens everywhere.
7. My keyboard now seems unable to remember that I want a comma to be kept as a user preference in the key to the left of the space bar. Bad UX.
8. My partner updated her s3 to 4.3 and had to change her screen saver because she could no longer read the icons in the top bar because the black background has been removed. A small detail but an unwanted and essentially forced changed. Bad UX.
9. If anything my battery is draining more quickly now. Marginal but noticeable. Certainly no improvement.