The thing is, writing term papers actually forces you to do research. After all, you’re in graduate school, which is training you to do research. The final exam usually just checks whether you’ve understood the concepts that have been introduced during the whole semester. However, the term paper is actually something different, it is a write-up of an exercise where the student is asked to apply the concepts that have been learned in class. In short, it’s a mini-research project.
I have to admit, the paper option is harder. One has to have an original topic at hand, and yes, I have seen professors schedule office hours in order to discuss possible paper topics with students. You don’t need that for the exam. However, for the paper, you have to actually scour a huge theoretical area in order to start writing a paper. No, scratch that, you have to then do research and see what has been written about it first, before writing the paper.
Now why am I still recommending this route? Because it will pay off in the end. If you already know what you want to specialize, then you can slowly tailor your papers to aim for that general research program. Who knows, these term papers might actually end up to be parts of your dissertation later on? Still, even if it doesn’t, then you will have more experience in doing research, and this term paper can be the beginnings of a conference presentation, and who knows, it might actually be a published paper in the future.
The logic is simple. If you take an exam, then sure, you study for it, and you pass. However, the benefit is short term. You might have an easier time getting a good grade, but in the long run, it will not give you practice in writing things and presenting them. When later on, you would probably be asked for a writing sample. If you haven’t written papers before, then writing one would be a hard endeavor.