Why does Ashkenaz start at Rachum Vechanun, and not say the first part (like Nusach Sefard does). What's the basis for the disagreement?
Viddui comes from the mekubalim and is recommended by the ARI. Minhag Ashkenaz did not adopt this addition to their siddur. Those influenced by the ARI did include it; among them are Sefardim and "Nusach Sefard" - meaning the Chassidic Ashkenazim. The basis for the disagreement is whether to accept Kabbalistic Kavanot into Davening or not.
Just an interesting side point, in Eretz Yisroel even Nussach Ashkenaz says the Viddui because Talmidei HaGra took it from the Sefaradim in Eretz Yisroel. They also adopted saying of the Ketores at the end of the weekday Shacharis for the same reason.