There is not such a fact. We have many dialects. But, Our government decides what kind of Japanese textbook should Japanese children use. So, children in any area can write standard Japanese.
Of course, some children know more kanji than others, and some aduIts remember kanji than other aduIts. But that is not related with area. Katakana is taught after Hiragana, so, small children use Hiragana only. But they soon learn Katakana. And they use Katakana following shool textbooks which are dicided by our government.