The Protestant reformation lead to the Thirty Years War and other religious wars, and much later also contributed to the Troubles in Northern Ireland. So, it's safe to say that the split between Protestants and Catholics led to much warfare. I can't remember reading about the same form of warfare after the East-West schism. I know of the Fourth Crusade and the attack on Novgorod in the Northern Crusade, but these seem to be outliers and does not point to any widespread animosity between Catholics and Orthodox Christians after the East-West schism? So, why was the Schism between Protestants and Catholics more violent than the East-West Schism, or have I simply not heard about Catholic-Orthodox wars?
I've written a bit about how the 30YW grew to be a very large and bloody conflict. If I had to drastically summarize, the rise of Lutheranism came at a time during which the Holy Roman Empire had to make concessions in the Peace of Augsburg that didn't address fundamental issues. Over time, those concessions, and the rise of Calvinism, led to a conflict that was viewed by many as rebellion against the HRE authority, into a religious war, into one that threatened the power balance of central Europe. Therefore, different parties entered the war on different sides.
To compare with the East-West Schism, keep in mind that that divide followed along the Rome-Constantinople division of the time. There were five major episcopal sees: Rome, Constantinople, Alexandria, Antioch, Jerusalem.