What happens when you start New Game+?
I have finished both branches at the end of the main game, and am considering starting a New Game+.
What carries over from the current game to the second playthrough?
Solution 1:
Absolutely everything but the story itself. You won't have any of your followers at first, but as soon as you hit the point in the story where they join you, (ie. when Slak joins, you get all your barbarians back) you can use all members of that class, with their levels, skills, and equipment intact.
Even Azra's level and tomes you collected carry over!