Referencing three of the following authors – Smith, Robespierre, Marx, Lenin, Marcos – define and contrast both Capitalism and Socialism. What are the core principles defining each system? What is problematic about each system? Which is better or more desirable?

Based on your question, I'll discuss Marx, Robespierre, and Smith.
History tells us that Maximilien Robespierre greatly admired the philosophies of Jean-Jacques Rousseau. Karl Marx himself was also influenced by Rousseau's socialist ideas. In fact, both Robespierre and Marx championed Rousseau's conception of democratic egalitarianism. They supported the abolition of private property and believed in Rousseau's idea of the "social contract," where the citizenry are afforded the right to replace a government that fails to secure their natural rights.
Robespierre and Marx viewed egalitarianism as the highest goal of a socialist state. In such a state, the government is (or should be) the defender of virtue and democracy. Marx believed that a socialist government should be first (and foremost) a proletariat autocracy. The proletariat or working classes would rule over the petty bourgeoisie and peasants, effectively stopping the ruling bourgeoisie elites from consolidating power in their hands.
Marx believed that wealth concentrated in the hands of a bourgeoisie elite few was morally wrong. Because the ruling elites controlled all enterprise, commerce, industry, media entities, and academic institutions in a country, the proletariat and peasantry would always be kept impoverished and disenfranchised. 
In Marx and Robespierre's socialist state, no one would own more than his neighbor. The state/government would apportion to each his need. Meanwhile, Adam Smith supported the capitalist ideals of a market economy, one that generates consumer choice, promotes economic growth, and increases production efficiency. Smith opposed the idea of mercantilism, where the government/state closely regulated industry and commerce. He believed that the government would be less efficient in apportioning economic resources than the private sector.
The core difference between a socialist and capitalist economy rests on who controls the production and distribution of goods and services. Marx and Robespierre supported the idea of a central planning entity regulating industry/commerce and then apportioning the resultant wealth to its citizenry. Meanwhile, Smith argued that an economy functioned best when market forces were allowed free rein, unshackled by burdensome government regulations and oversight. Smith believed that the best way to bring about freedom, democracy, and prosperity was to allow the inherent self-interest of human beings to flourish.
Smith maintained that self-interest and self-preservation were key motivators in facilitating economic growth. He argued that individuals would care more about their own welfare than a labyrinthine bureaucratic state. 
So, Marx, Smith, and Robespierre believed in equality, democracy, and freedom: they just disagreed on how to realize these goals. As to what is problematic about socialism and capitalism, I would argue that both share a similar weakness: the predilection of an elite few to appropriate all power and wealth towards its own purposes. You may have read Orwell's works, specifically Animal Farm and 1984, in your school/college readings. 
In Animal Farm, Napoleon ousts Snowball. While Snowball is a subtle portrayal of Trotsky, Napoleon epitomizes a composite of Lenin and Stalin. You may recall that, under the leadership of Napoleon, the pigs eventually become no different from the abusive and greedy human masters who previously ruled the farm. Snowball's Trotskyian ideals are eclipsed by Napoleon's brutality. Thus, in both capitalist and socialist economies, there is the danger of power and wealth becoming entrenched in the hands of an elite few. In such a situation, it matters little whether a central planning state or a free market economy controls industry and commerce. The populace will remain disenfranchised and marginalized.
As to which system is better or more desirable, I hope that my answer helps you to make that decision for yourself. Thanks for a thought-provoking question!
 
 
 
 
 
https://www.historytoday.com/archive/robespierre-and-terror

https://www.marxists.org/history/erol/ncm-7/lenin-socialism.htm