These words are not interchangeable in absolutely every context; for example, it is idiomatic to say that a student is receiving "financial aid," but not that she is receiving "pecuniary aid." We also wouldn't refer to "the global pecuniary system" or "the pecuniary crash of 2008."
However, they are indeed close synonyms, and there are many contexts in which you could safely substitute one for the other. For example, "He is having financial difficulty" and "He is having pecuniary difficulty" are equivalent in meaning.
That said, the two words are by no means equally common. In the modern United States, at least, I believe that "financial" is both much more widely used and more widely understood than "pecuniary," and this Google Ngram seems to bear that impression out.
To some, "pecuniary" may also sound a bit old-fashioned. It seems it was more common than "financial" in the early part of the nineteenth century, but has been less common since about 1870.