Which title?
It doesn't happen much anymore, but into the 1960s it used to be quite common practice to retitle films crossing the Atlantic: changing American movie titles in Britain, and vice versa.
Normally I prefer the original title of a film, but in a few cases an alternate title seems more fitting. The case of The Battle of the River Plate is a close call to me. But the US title, Pursuit of the Graf Spee, strikes me as a slightly more apt title.
For one thing, it more accurately describes the action of the film. The picture is about the Royal Navy's pursuit of the German vessel, only one part of which involved the actual naval engagement. Most of the film centers on the chase, the later efforts to dislodge her from her safe harbor in Uruguay, and the Graf Spee's final actions. The film, in short, is about much more than the battle alone, which is of course a crucial event but only one portion of the overall narrative.
Also, "pursuit" is a more active, dynamic word, indicating movement and speed, while "battle" -- its reference to blazing pyrotechnics notwithstanding -- is a somewhat static term, lacking the sense of flow and plot development better conveyed by "pursuit".
Obviously this is one of those things where there's no right or wrong, and I'm sure most fans will prefer the original UK title. That's certainly not a bad or inappropriate name, but after much thought I come down narrowly on the side of the American retitle. As an American, I first saw this movie at age 8 or so under its US name (the American print is otherwise no different than the original British film, not edited in any way), but when I learned its actual title years later I rather liked it, and still do. But "Pursuit" gives a better impression of what the film is all about.