In practice, researchers often do not know in advance how helpful archival research is going to be. This means that one advantage is that you may discover something unexpected which will confirm a hypothesis, change the course of your research, or save months of work, and one disadvantage is that you may discover nothing you could not have found online. The archival method of research is a gamble. This is also true of conducting research online or at your local library, but the stakes are higher, particularly if you have obtained a grant and traveled around the world to conduct research at a particular specialist archive.
One of the great advantages of the archival method is that you can obtain types of material that would not be available any other way. If you are conducting high-level research on a well-known writer, for instance, there will probably be at least one archive which has hand-corrected manuscripts, first drafts, and letters describing literary progress. Sometimes you might be the first person to read these. Occasionally, archives do not even know what they have in their possession, and you might discover hitherto unknown works. Archives offer a way to break new ground as a researcher.
On the other hand, the old tin trunk covered with dust may not contain anything of interest. Conversely, the archive may be meticulously organized, to the point that everything they have has already been picked over in detail by twenty other scholars. Finally, the archival method is much more worthwhile for some types of research than others. In history and biography, it may be vital, whereas in philosophy and the sciences, it will mainly be useful in providing subsidiary information.