I have had a Note 2 since one week after Thanksgiving when it finally came to Verizon, and I have never had an issue I could not resolve. This has been the most powerful and stable phone experience I have ever had. I play games daily, spend about five hours of my day working on my phone professionally, and I still do not have to charge it until after midnight. I get over 19 hours of use on my phone daily, with about 7 hours or more of that time being actual app usage, and thirty minutes being phone usage.
I have a Verizon note 2, unrooted, and I disable the bloatware that verizon puts on it. That, and a clean install of Clean Master and Battery Doctor and Lookout for maitenance. I run 6.3 gigs of apps, and hit almost every one of them every day.
If someone thinks they can get Note 2 performance standards on a dual core ARM 1000MHz processor with 1 GB of RAM, powered by a 1735 MaH battery - they frankly are emotionally attached to an old phone, or do not know what they are doing. I have no inclination to insult anyone, it is just facts are facts, Electronic engineering is a Science, not a sentiment or branding. The note two is bigger and clocks faster in every way. The only possibilities of that happening is mechanical defect which is covered by warranty, physical damage to the unit, system invasion or corruption by malware (which anyone who knows what they are doing can detect and prevent), or it was screwed up in rooting or flashing a custom ROM: in short, Defect, damage, or user error. If you still had your note 2, and lived near philly, I'd say meet me, I'd pop the hood on it and you'd be suprised by the improvement.
I think browser hanging is actually one of the easiest things to solve on the phone. It has something to do with encoding on some international websites, and it is not limited to Samsung.
Option 1: Clear cache, uninstall updates, disable - turn off, then turn back on, enable browser, update.
Option 2: install Dolphin. It works really well on international websites.
I can optimize most phones, and the samsung experience seems intuitive to me - though I do not use multiple panes on my phone. I use a home screen and only build secondary pages when I need them (like making a games one for a road trip, or a page dedicated to a client.)
In fact, I can make TouchWiz work very well for me - especially with how nice it plays with Zooper Widgets. I also run Nova Prime tho - and have everything home, because well, why not?