[Update: “…without spending an extra $180 on a third-party tool that unlocks hidden, unsupported functionality”]
Layout a sentence that contains a mixture of English and Japanese.
In Word, you can say “use this font for Japanese characters only”, automatically leaving the rest of the sentence in a more-appropriate font. If you want to do this in InDesign, you must assign a character class to each string of Japanese text, or else layout the whole sentence in the same Japanese-capable font.
And that character class will not be applied if the sentence is used in a running header. Which means that you cannot use character-class-based styling in text that will be used as a header.
The workaround, which doesn’t work, is to use position-based nested styles in the header.
The workaround for the workaround, which doesn’t work, is to use regular-expression-based styling in the header. You can do something half-assed with regexps in a normal paragraph style, but the exact same regexp that works in the body text doesn’t work in a header style; the regexps are apparently applied before the variable substitution (which, come to think of it, is likely the problem with nested styles as well).
You can probably do Word-style font-mixing in the Japanese version of InDesign, along with vertical text, furigana, and all of the other things Word gives you in all versions, but I can’t buy that in the US. And, frankly, it’s far too expensive to ever consider trying to import a copy just to get potentially prettier printouts than Word.
[Update: it is claimed in a number of places that all of the Japanese functionality is present in the US version of InDesign, but that none of it is exposed in the UI. So, if someone sent you a document made in the Japanese version, you could print it, but not edit it. This suggests that it would be possible to export such a document to either the Tagged Text or XML formats and do some scripting work.]