Downloadable version are easier:
To reuse your save, you must rename your newly downloaded file same as the one you saved your game, as well as putting it into the same directory of your previous file.
It is more complicated to get web version's save to work for newer version. You have to find and replace new save by locating the path much like below:
Newgrounds save location (Firefox):
C:\Users\[user account name]\AppData\Roaming\Macromedia\Flash Player\#SharedObjects\[RANDOM LETTERS]\uploads.ungrounded.net