...Whether a country which issued a visa into the old passport will accept it if you show it along with the new passport is a question that you'd want to direct to the embassy or consulate of that country.
Indeed, since there is no worldwide standardization of this sort of thing. Chilean entry permits for U.S. citizens (and those of a few other countries that charge Chileans for visas) are explicitly good for the life of the passport to which they're attached. If you get a new passport, for any reason, you need a new entry permit too.