Are there parallels in the arguments of Theodore Roosevelt's New Nationalism versus Woodrow Wilson's New Freedom to modern debates in American society?

The America of 2019 does not strongly resemble the America of 1912, so the parallels between the two eras are, at best, tenuous.
In 1912, voters had to choose between Theodore Roosevelt's New Nationalism and Woodrow Wilson's New Freedom in a presidential election. (There was also a third option—the incumbent William Howard Taft.) Even though Roosevelt lost the election, most of his agenda was implemented by Wilson. Both men were presidents during the Progressive Era and shared key ideas and goals. They believed the central government should be a strong and positive force for national betterment.
Roosevelt and Wilson both favored strong corporate regulation. For instance, both men opposed child labor. The 1900 census revealed that nearly twenty percent of children worked. Roosevelt had formed the National Child Labor Committee (NCLC) in 1904 to combat the practice of child labor. In 1916, under Wilson, the first child-labor law was passed.
Both men also used their presidential powers to promote environmental protection. Roosevelt loved the outdoors and was a champion of environmental protection. In 1916, Wilson signed a law which created the National Park Service.
Today, by contrast, the parties do not have similar views on strong corporate regulation or environmental protection. Comparing different historical periods is usually fraught with difficulty.

Theodore Roosevelt's New Nationalism featured things like increased military spending, easier access to voting, social insurance, voting rights for women, etc. Wilson, on the other hand, sought to shrink governmental involvement in national affairs through reform bills that were designed to help the average American. His stance on tariffs and taxation is certainly relevant today, as the Bush-Clinton era dealt heavily with taxes for the rich and the poor, while Wilson was more concerned with the average American, perhaps due to the fact that the wealth gap back then was not as large as it is today, with the top 1% controlling about 40% of the private wealth owned by this nation's populace. So taxation would be the most resonant feature of both Roosevelt's and Wilson's economic and social policies today.
https://en.wikipedia.org/wiki/New_Nationalism_(Theodore_Roosevelt)

https://en.wikipedia.org/wiki/The_New_Freedom

The Election of 1912 featured Theodore Roosevelt, leading his newly formed Progressive Bull Moose Party, and Woodrow Wilson, leading the Democratic Party. Although he officially ran as a Democrat, Wilson is also considered a Progressive candidate, supporting numerous Progressive reforms of the era. In general, the Progressive movement sought to eliminate new social, political, and economic problems caused by industrialization, urbanization, and immigration through local and national reforms. This election therefore represented a contest between two candidates who espoused competing strands of Progressivism, which were expressed in their party platforms. Roosevelt centered his campaign around his New Nationalism platform, while Wilson called his platform the New Freedoms.
The key differences between New Nationalism and New Freedom are evident in their stances on the government's role in the economy, business regulation, and social reforms. Roosevelt's New Nationalism called for a federal government with strong regulatory powers; however, he felt that there were some "good trusts" and therefore was opposed to using the government to break up all monopolies. Wilson, on the other hand, sought to end all trusts; however, he felt that state governments rather than the federal government should be responsible for regulations. In addition, Roosevelt advocated broad social reforms such as women's suffrage, minimum wage laws and shorter work days, whereas Wilson supported a more free-market economy with an emphasis on small business. These debates continue today, with Democrats and Republicans often split over the power of the federal government, especially its powers in regulating business. Democrats typically favor a more powerful federal government that regulates businesses and large corporations, while Republicans often favor a smaller, less involved federal government, preferring to leave more power to states. In addition, Democrats typically favor more social reforms and social welfare programs.