A few major differences:
- Trump labels China and Russia as
"Revisionist powers...that use technology, propaganda, and coercion to shape a world antithetical to our interests and values" -Trump
Though while this much more antagonistic, Obama made somewhat similar but veiled statements:
"Strengthening our enduring commitment to a free and peaceful Europe by countering aggression and modernizing the NATO alliance to meet emerging threats." -Obama
"Rebalancing to Asia and the Pacific through increased diplomacy, stronger alliances and partnerships, expanded trade and investment, and a diverse security posture." -Obama
Both of which are clearly aims at containing Russian and Chinese influence in their respective regions.
- Trump names "Jihadist Terrorists" as a threat, a phrase akin to "radical Islamic terror" which Obama refused to use
"Jihadist terrorists that foment hatred to incite violence against innocents in the name of a wicked ideology" -Trump
- Trump's Nation Security Strategy names Realism as the ideology behind the strategy:
"The Strategy articulates and advances the President’s concept of principled realism. It is realist because it acknowledges the central role of power in international politics" -Trump
I personally found this very interesting, Realism is a very self-interested ideology (from a state perspective) and the whole of Trump's Strategy reflects this. While Obama's Strategy does not name an IR theory that defines it, the emphasis on cooperation and careful sidestepping of naming anyone as an enemy is much more indicative of Liberalism
- Trump calls upon US allies to pull more weight from a security perspective:
"America’s allies and partners magnify our power and protect our shared interests. We expect them to take greater responsibility for addressing common threats." -Trump
- Obama names several programs and initiatives for helping development of less-developed countries, a theme absent from Trumps Strategy:
"Leading efforts to reduce extreme poverty, food insecurity, and preventable deaths with initiatives such as Feed the Future and the President’s Emergency Plan for AIDS Relief." -Obama
"Promoting and defending democracy, human rights, and equality while supporting countries such as Tunisia and Burma that are transitioning from authoritarianism." -Obama
"Building upon the success of the U.S.-Africa Leaders’ Summit by investing in Africa’s economic, agricultural, health, governance, and security capacity." -Obama
On the whole, Trump's Strategy is more aggressive and centered around his "America First" policy, whereas Obama's was more focused on international cooperation and development. The Realism-Liberalism juxtaposition mentioned earlier provides a lot of insight on the lens through which each president views the world.
Both called for increases to the military and a more competitive economy in their own ways.