It's by choice. After beating the final boss, you should end up in an area called 'My Room', which is basically the hub for the animation viewer. At any time you can leave and continue to wander around the main game's map.
I forget exactly how you go into NG+ though (been a long while since I actually sat down to play), though it should be mentioned in the thread somewhere...
EDIT: ok, so sat down and beat the final boss again. After the credit roll, you'll end up in a room with a door to the left (Leads back to the save point right by the final boss room), a save crystal, a set of stairs going up, and one of those green pools.
The stairs go up to a pair of healing points (red and green) to the left, and to the right is a door that leads to 'My Room', another set of stairs, and a blue crystal that basically allows you to adjust a few things (only thing I'm sure on is changing how much HP/MP you have).
At the top of the second set of stairs is a red crystal that'll let you start NG+. It'll give a bunch of options as to what you want to carry over, and selecting the option in the pink box to the right will start NG+
