:::::Halsall's article is 20 pages long (pp. 35-55). So there is a lot more to it than the two-page PDF. He may complain about the term "Barbarian Invasions," but it's the one he uses. As for Delbrück, I think its significant that the main current translation uses "Barbarian Invasions." After all, we want to follow English usage and not German. Even while Britannica's "ancient Rome" article uses "Barbarian Invasions," their "Germany" article uses "Migration Period." So it's primarily a question of whether you're viewing events through the Roman or German end of the telescope.