I loved NG+! I pretty much destroyed AC on Hard Mode and jumped straight into NG+. What a challenge it was too; no visual clues, mixed enemy units, less hiding places, more aware enemies... and the goddamned Batman to kick the shit out of them! With the occassional help of Catwoman, of course.
Also, since you don't have to hunt down Riddler trophies if you've done them all during the standard game, you can focus more on the story itself. Since I didn't get sidetracked the second time around I had a much clearer understanding of what was going on.
The story ending though... GAH! It still gets to me. It shocked me the first time around, and the second round I found it all the more gripping. The little hints along the way, the visual clues (use your enhanced vision during on specific fight for example...). Did anyone catch that little throwaway line about a specific supervillain which turns out to be all important? God, how could I have missed that all the first time around? So did the worlds greatest detective, but usually I am a bit more genre savvy about this.
Now I only log back into AC on occassion just to talk to the calendar man. I've set my console clock a bit back several times, since I missed out on thanksgiving and christmas. Creepy guy that, I never took him that seriously, but AC turned him into quite the dark character.