They're not interchangeable. 'Nonsense' is used to describe something that is illogical or wrong, and 'gobbledygook' is used to describe something that is difficult to understand because it's very complicated. I've never used or heard the latter (I've seen it written, though) but I say and hear 'nonsense' very often.

"nonsense" is informal and very casual. We hear a lot in our everyday communication. 'gobbledygook' often describes something said by polititians. Polititians like to make what they say sound very serious. They'd like to use a very complicated word which is very difficult to understand but common people would use a totally different one which is easy to understand and less serious but which means exactly what a polititian wnat to say.

Nonsense is used more often. It also is logical: "non-sense" Gobbledygook is exactly what is sounds like. It means something hard to understand (writing and speech) because the words are complex or you don't recognise them - as though it would make equal sense if the speaker were saying "gobbledygook, gobbledygook, gobbledygook"!

'Gobbledygook' is an informal word used to talk about a complicated language that is difficult to understand, especially when used in official documents, or to refer to jargon that is impossible to understand. However, we use 'nonsense' to mean 'ideas, statements or beliefs that we think are ridiculous or not true' or to talk about 'spoken or written words that have no meaning or make no sense'.