There are several different reasons internal or external are better. Some of that depends on your coop and some on your personal preferences. Cold is not an issue for the birds themselves, but the eggs might freeze easier in an external nest in winter. Some of that is how you build it. If you insulate remember they will eat many different kinds of insulation so you need to cover insulation with something they can't eat.
Heat is generally your biggest enemy toward a chickens health compared to cold. If your nest is exposed to a sunny side it might get pretty hot. You don't want them laying in an oven. An external nest will warm up faster than an internal nest if it is on the south side for you but I'd prefer the nests of either type on a cooler shaded wall. So think freezing eggs in the winter or cooking hens in the summer.
Internal nests are easier to keep rainwater from getting in them, but of course with flashing and caulk you can make your external nests rain-proof. A door to gather eggs on the face instead of on top can help with rainwater issues.
If you have a small coop and space is an issue, an external nest frees up more room inside the coop.
A poorly constructed external nest can be an entry point for a predator. Of course you solve that by building it stout.
Some people like the appearance of an external nest. With paint you can make them a focal point of the coop.
You can build internal and external nests so you can gather eggs from inside or outside either one. It depends on how you construct them. To me that is a non-issue.
That's all I can think of right now. The chickens won't care, what makes you happier?
