The question would be difficult to reach an answer because there is no other similar case, to my knowledge, commonly using two distinct set of letters that have equivalent phonetic values outside those bicameral writing systems and Japanese. In both cases, relationship between sets are conventionally and discretely defined, not such that a general ground has been established.
In defense of this traditional idea about hiragana and katakana, I can at least say that they are different in graphical origin. Though they both derive from kanji, hiragana is made from whole-character cursive forms, while katakana taken from partial forms of kanji. All other systems where multiple styles might be mixed, including Latin alphabet, Georgian alphabet and Chinese characters, are historically unilinear i.e. one style developed into another and so on. In this sense, German before WWII might be qualified to be a mixed digraphia in a certain degree, but they share the same graphical origin. A more accurate analogy to hiragana and katakana is letters in Coptic alphabet, which are from Greek and Demotic, two separate descents of Hieroglyph, except that they merged both sets into one rather than keeping two tracks.
Note that although hiragana and katakana have been standardized to be almost parallel in the 19th century like the way they are now, their difference was historically much more substantial. The set of currently called hiragana was far bigger than katakana due to homophonous variants (変体仮名); they had different collection of orthographic ligatures (合略仮名) because of graphical difference; they were used in distinct social settings and not usually mixed together.