The New Freedom and the New Nationalism were both reformist and Progressive visions. That is the main thing they have in common. What is different about them is that Roosevelt's New Nationalism envisions a much larger and more permanent role for government in the regulation of the economy.
Both of these plans were aimed at restoring a more egalitarian America. Both were based on the idea that large businesses and their owners had become too powerful. Both, therefore, aimed to reduce that power.
Roosevelt's vision was of a government that would step in and regulate business so as to achieve social justice. The government would do things like setting minimum wages and would generally oversee the workings of business to ensure that it did not harm anyone.
Wilson envisioned a much smaller role for government. For him, the government's job was to break up the trusts and the concentration of power on Wall Street but then to get back out of regulating business. Wilson believed that once the big firms were broken up, small firms would compete and all would be well. At that point, the government could step back.
Both plans called for governmental efforts to increase social and economic justice, but Roosevelt's called for a much larger and more permanent role for the government.