The most noticeable difference is that the screen of the new version is more evenly lit. The 1st generation Paperwhite tended to show uneven areas at the bottom of the screen where the lights are situated.
The New version has add reading enhancements like being able to go to references without leaving the page you're reading as they appear in a pop-up window. Also, you can skim forward and backwards in a book in a pop-up window, again not moving from your current page and not changing the furthest page read.
There are other differences, like Cloud Collections but that's a whole other discussion and very controversial.