After using the new iPad 3 for a day, I can tell you that I adore the new Retina screen. This improvement alone is well worth the upgrade.
Text is so crisp and clear, even tiny letters on zoomed out webpages are still very easy to read. Because of this, reading for a longer period of time on the new iPad is far less tiring for the eyes. I have also noticed that I haven’t touched the ‘Reader’ button in the address bar of Safari once until now, while I did this all the time on my previous iPad for better readability.
An other improvement that I like very much is the better upscaling of iPhone apps on the new iPad. I still use some iPhone apps on my iPad because there is no (good) iPad alternative. On the new iPad, these apps are a joy to use and very readable, especially when you open a webpage in an inline browser.