There's no inner dispute in Judaism of Ashkenazi vs. Sephardi. Despite the ranting of those who don't actually personally know any charedim, nearly all Ashkenazi charedim respect Sephardi tradition, and vice versa. In fact, the two main pillars Jewish law, the Shulchan Aruch and Maimonides, are both Sephardi, and are studied intensively by all religious Jews, including all Ashkenazim.
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from the article: Analysis / The ultra-Orthodox are returning Israel to the middle ages