But I'm curious. Is there really any difference in content? Is the translation in any way competent?
First, congratulations on an excellent movie selection!
Second, let me try to unpack this coherently: The American version basically hits all the main story beats of the Japanese version, but does so through the narrative of American reporter Steve Martin (played by Raymond Burr!) whose scenes were fairly cleverly inserted into the original film in such a way that it "localized" it without having to overdub all the Japanese dialog in the movie (as later Godzilla films would be notorious for). There is some additional material in these segments that isn't in the original, but not anything that adds any real substance to the story, more like just explaining key scenes from the original film.
I might be slightly biased, but I do feel like the American version is worth a watch, if only to see a fairly well-done attempt to make a foreign film accessible to American audiences that may have otherwise skipped a subtitled unedited version.
That said, the original Japanese version really is a moody and effective film, a true classic of the genre, and I would highly recommend it!
(Incidentally, compare and contrast this to the Godzilla (1984)/Godzilla 1985 dub job, which is a whole other story...)