I find that whenever I start a second playthrough of a game, I tend to just pick the new game option. Especially if the first playthrough was years ago, a new game + would make me feel like i'm playing with "someone else's inventory". Like you started up a previously existing game from a rental.

There are a few exceptions, like Chrono Trigger, where starting up a new game after the first playthrough can help you see different endings pretty early on in the game and give you an alternate playthrough.