This answer says "... it should be possible to cut into the wall and install a metal box (don't use plastic, please) [for an outdoor outlet]."
What are the problems associated with using a plastic box for an outdoor receptacle?
The problems are not specific to an outdoor location. They are for any use.
Top 10 reasons metal boxes are better than plastic boxes:
And # 11: Because my electrician (who has been in the business for a long time) and Harper both say so!
UV light from the sun destroys plastic. For regular plastic, it's a matter of years or decades before sun will make it brittle and crumble into dust on a slight touch. You don't want your receptacle box to crumble into dust.
Also, that's more of an opinion than hard rule. There are outdoor receptacles made of UV-resistant plastic, but they're clearly marked (and priced) as so. As I understand this warning, it's aimed against repurposing common indoor boxes for a duty they're unfit for.
If you're talking about a house as a service plug or simply just an outside outlet, plastic is perfectly acceptable. Just make sure you're using a weather-rated outlet and cover.
This is all related to residential work.
Despite what the other answers may suggest, you are going to be mounting them inside of a wall. This means that they are not exposed to UV Light and extreme temperatures. And wild animals will certainly not be chewing on your boxes.