The question is "Why is the God of the Old Testament so violent when Jesus in the New Testament is so peaceful?" First of all, the question reveals a fundamental misunderstanding. God in the Old Testament is full of love and peace, but he has to judge evil. God in the New Testament is no different.

The Old Testament is the story of a nation; the New Testament is the story of a person. There are different things going on. Violence is a normal part of a sinful world and will never go away. Sometimes the only way to not let violence take control is to meet it with a "bigger sword." As long as the use of force (1) has a legitimate basis, (2) has a moral end, and (3) has a justifiable means, a qualified use of force is not only necessary but justifiable.