Of course, there is going to be a set similar considerations: mastery of local language, cost of living vs. your budget being central.
But I always say that one shouldn’t shop a graduate degree abroad as one would an undergraduate study abroad.
One has to pay attention to the job market (and the academics as well) at your destination when one does a graduate degree abroad, whereas it is (much?) less of a concern for undergraduate study abroad.
And, in graduate school, travel is much more dependent on your academic activities (conferences, summer schools, etc.); I lost count of the number of people undertaking study abroad in Europe with intensive travel as their primary if not sole objective (and that didn’t major in anything that actually warranted it, such as art history, international relations, history, area studies…)