BG:EE adds npcs, classes, kits, and item fixes that will not transfer to the old BG2. I'm not sure if would crash or exhibit other weird behavior from importing a save game with state flags from new quests, items, spells, classes, etc.
The safest way to continue the story in Baldur's Gate II if you are using the old/current edition is to recreate your character. When you meet NPCs from the previous game, they will give you the chance to choose how you dealt with them in the past via dialog. The game strips all your equipment when you first starts regardless of what you import with, and then will continue to offer better gear over the course of the game than what you can get in BG1/BG:EE. The only class that will end up having to spend more gold early on will be a Wizard, who won't have a complete spellbook despite starting at a higher level.
Or just wait for BG2:EE. The only reason not to wait for BG2:EE would be because there are some mods out there that won't be available for BG2:EE for quite some time (or ever) due to the changes to the engine and fixes implemented differently from what cross-mod compatibility efforts used to deal with.