This is a question that falls into one one of those categories that straddles the contradictory line between the deceptively simple and the insanely complex. This conflict was more than just two ideological systems in competition with each other, and the Cold War was only one component of this struggle. Moreover, neither communism nor capitalism were discrete, homogeneous sociopolitical and ideological systems. There were many different forms of communism just as multiple capitalisms. The free market entrepreneurial capitalism championed by the United States was different than that of postwar Japan or West Germany in which there was a good deal of cartelization and a close relationship with the state. By the same token, Soviet communism was quite different from what later was known as Eurocommunism or the Maoism of China or North Korea's Juche. The Cold War was not just a struggle between two superpower-led blocs, but also contained many different struggles within these two blocs.

With the above caveats in mind (and also bear with me this is an extremely simplified narrative), the two systems were at their core somewhat incompatible. Many communists derived their understanding of the workings of the capitalist system from the works of Karl Marx who held that capitalism was a historical epoch whose many contradictions would prove to be its own undoing. According to Marx, while capitalism buried the old feudal order it was inadvertently laying the foundation for its workers to rise up and form an new society. Part of the romance of communism was the idea that through revolutionary action, humanity could emancipate itself from the larger historical trends that has plagued mankind since the first organized human societies. The goal end goal of many self-described communists was communism, a utopia characterized by a higher quality of life, ample free time, and a social leveling in which there would be no rich or poor people. While Marx predicted this utopia, he left no real blueprint as to how to reach it. How to reach real communism would become one of the major fracture lines in the communist movement in the century and a half since Marx and Engels wrote the Communist Manifesto. Some radicals supported a violent revolution led by the industrial working class in which the "dictatorship of the proletariat" would enact socialism which would create the socioeconomic foundations for a communist society. Other Marxists would argue that the ballot-box was the agent of revolution while still others would argue that transformations in individual thought would allow for a broader transfiguration of the human condition. But many self-described communists felt that history was on their side. The Soviet Premier Khrushchev once famously told a group of Western ambassadors that he was confident that capitalism's days were numbered. Often mistranslated in the West as "we will bury you," a better translation of Khrushchev's rough language was "we will be present at you funeral," but both phrases capture something of the confidence communism had in its future.

In contrast, capitalism tended not to have as rich of an intellectual heritage as Marxism. There were certain prophets of the free market such as Adam Smith, the Chicago school, or Ayn Rand, but the strength of capitalism was not in its treatises or thinly-veiled author tracts masquerading as novels, but in the explosive growth of capitalist economies. Pace Marx's predictions that capitalism would grow meaner and more desperate, the system itself seemed to grow and become more entrenched. There were still the poor and the exploited, often in marginal elements of the population or globe, but there was also a burgeoning middle class and a new strata of hyperrich. Additionally, the capitalist system was adept at producing and marketing consumer goods (or as one prominent historian of consumption calls it "stuff") to an ever widening component of the population. In the US, the success of this supposedly free market meant capitalism became closely associated with American political values such as freedom and democracy. While there were more than a few Americans who saw the acquisition of wealth by private businesses as antithetical to these values, there was a strong subset of American political thought that by mid-century saw the free market and democracy as working hand in hand and it was the American mission to ensure the global success of this system. A good window to this particular zeitgeist is the 1954 Warner Brothers cartoon "By Word of Mouse" underwritten by the Sloan Foundation think tank. The cartoon's streetwise American mouse extols the virtues of mass consumption and mass production to his old-world cousin and conveys something of the "mission" which the some in the US saw the free market as playing for the world.

But it was not just two ideological systems for organizing society that were at loggerheads during the Cold War, there were also other contingent factors at play pushing these two against each other. The experience of the Second World War inculcated a mentality that made it much harder for either side to push for pure peaceful coexistence. The experience of both Munich and Barbarossa underscored to many that compromise with an ideological enemy was dangerous (expansion of this point- both the Munich Pact in which Britain and France made a deal with Hitler in 1938 to avoid war and the German invasion of the USSR in 1941 had a long-term impact on the foreign policies of both the USSR and US. The "lesson" of both was that some enemies cannot be bargained with and these fatal miscalculations nearly led to Hitler's victory.) Partisans of both capitalism and communism selectively interpreted Hitler as an ideal other was now being carried out by their rival. Communists saw the German dictator as a byproduct of the social forces of capitalism and all of its worst instincts while more than a few partisans of the free market saw the all-encompassing single party state and dictatorship of Hitler as little different in content than that of Stalin or Mao. By the same token, victory over Hitler added a vindication for both systems in that they had triumphed over an enemy that represented the antithesis of each system. But victory came with significant material and human costs and both sides were desperate not to lose their hard-fought gains. The advent of nuclear weapons added an existential danger to this competition with the fear that a misstep or apathy could lead to a one-sided annihilation. The collapse of European empires in Africa and Asia, as well as instability in Latin America, added a further wild card. For many observers after 1945 it appeared that the whole world was now up for grabs. This was expressed in the term Third World, coined by the French theorist Alfred Sauvy; the First World (US-led North America, Oceania, and Western Europe) and the Second World (USSR and Eastern Europe) were already claimed, but the rest of the world was up for grabs. Dangers and opportunities in the Third World intermixed freely in the geopolitical formulations of the Cold Warriors.

This paradoxical mixture of fear and overconfidence underlay why neither side could ever really mind their own business during the Cold War. There were people on both sides of the Iron Curtain during the Cold War that wanted a less strident form of competition, or in the words of the musical Chess, a period in which "the Berlin Wall becomes a backyard fence". Yet both systems never suffered a shortage of "hawks" that always pressured for a more proactive policy, whether to take advantage of the other's perceived weaknesses or prevent their rival from gaining a foothold. Internal weaknesses within the Second World, especially as the planned economy sputtered, added a further level of weaknesses to the Communist bloc. But if the Second World seemed to stagnate, there was increasing concern within the First World that the apparent success of Marxist-inspired political movements such as Kwame Nkrumah's African Socialism or Ho Chi Minh's communist insurgency meant that capitalism was on the verge of losing the Third World. For both sides, decision-making processes and leadership cultures were conducive to worst-case scenario thinking that interpreted world events into a grand zero-sum game. Fears of nuclear destruction, diplomatic channels, and even common human morality acted as a check against escalating the Cold War beyond competition and proxy wars, yet this potential for the Cold War to escalate into direct hostilities was always there.