What are the differences between the original and the re-cut versions of Psycho-Pass?
The new edit version of Psycho-Pass has:


Reanimated Opening and Ending themes
Additional minor scenes (for example in episode 1 there are two new soliloquies not seen in the original). These tend to be placed midway during the episodes to allow for a better transition between the two old episodes.
Redone animation of particular scenes (and some additional CGI in places)
Some music changes in scenes


There's nothing substantially different in the new edit version, so if you have seen the original there's not a huge benefit in watching this version and you should still be able to watch the sequel Psycho-Pass 2 in Fall 2014 without worries.