Upvote:3
You can show a new passport and the visa in the old passport - that's OK both with the Schengen countries and the US:
Per TIMATIC, the database used by airlines:
For the US:
A passenger may enter the USA with a valid visa in an expired passport, if also holding a valid passport of the same nationality
For the Netherlands (same rules throughout Schengen):
Valid visas in full, invalidated travel documents are accepted if accompanied by a new travel document
So no, you don't need to get new visas in your new passport.