The reason I bought The new iPad is because my 1st generation iPad's app always crashed on iOS 5.1. Seems like there was too less RAM to do decent web browsing on the new iOS. It was working fine 2 years ago, but I guess either the websites got heavier or the iOS got heavier, I'm sure it was lack of RAM space available.
I'm using a case by Logic3, and it has rubber grip, which I am pretty fond of. I'm planning to get another case soon, but finding a really good case is pretty hard, and there are a LOT of choices and it can be pretty expensive so I'm going to carefully choose it.
What changed the most for me is the Evernote experience. I use Evernote a lot, (I've even talked to Evernote CEO, Phil Livin personally in the past) and writing new notes fast is a really good thing for me.
The fast dual core processors are really a plus as it makes web browsing ultra snappy, and I'm glad I bought The new iPad.