Is there any reason to play Batman in story plus mode?

I finished "Batman: Arkham City" last night. So after that, New Game mode opened as "Story+".

Why should I play that? What differences are there between this and the main story mode?

Solution 1:

There are a few differences between the two modes.

• Enemies do more damage and have better AI
• Enemies have upgraded equipment
• No counterattack indicator

You start off with all the upgrades from your Normal/Hard playthrough. Riddler trophies also carry over.

The only "tangible" reward you get for completing the game in New Game+ mode are the two achievements Twice Nightly, for finishing New Game+, and Perfect Knight - Day 2, the requirements for which are listed in the question I just linked. Otherwise, it's just there if you want to play through the game again with more challenge.