Oh, maybe that's what DS2 said and I've already forgotten what DS1 said when I finished it. All I know is I'd just finished it, anticipating playing DS2 next, when this "Ok, now you can play it again blah blah blah..." message came up. I didn't really pay close attention.
If you want to keep all your upgrades, you have to play the same difficulty level again. The second time through is good though, because then you can make sure everything is upgraded to max. Also, you might use weapons the second time through that you didn't use the first time.
That is how my second playthrough went.