As a student of history I would examine the two ideologies thusly.
Communism: A system of socio-political organisation created by Karl Marx and Friedrich Engels.
The first time that this ideology was ever ‘implemented’ was Russia after the deposition of Tsar Nicholas II. This is the traditional reading of history, however the system implemented in Russia was not Communism as advocated for by Marx’s and Engels’ instead it was a modified variation of the ideology known as Leninism, created by Vladimir Lenin in order to harness the power of the uneducated Russian peasantry. After the institution of Leninism we saw the infamous reign of Stalinism, and in China a parody of Stalinist ideology by Mao in Mao Zedong Thought.
All these variations however are not what one might regard as ‘pure Marxist Communism’, there are key subtle adaptations made to the ideology and it can be argued that many of the key failings and criticisms of Communism may instead be attributed to these ideological modifications.
Leninism: Key modifications to Marxism here include: that the revolution should be forced and led by a revolutionary vanguard of professional revolutionaries.
Stalinism: Major modifications to Marxism here, primarily the modifications relate to solidifying Stalin’s absolute hold on the reigns of power. Therefore the main alterations include the increase in levels of state control, forced collectivisation and the ruthless elimination of all opponents.
Maoism: Mao largely followed the Stalinist model, so the points above are all relevant, however one can argue that in regards to the cult of personality and government control over the work force Mao had greater control.
Therefore it is very difficult to compare the actualities of Communism and Capitalism, since it can be argued that there has never been a Communist state in the strictest sense. Especially when we further consider that according to Marx Communism was a state in which there was no government and that such an apparatus would simply wither away. In order to be accurate we should instead say that Communist states are Socialist states, the type of state according to Marx that was the prelude to a Communist state.
Capitalist: A state centred around the idea of free trade and industry in the hands of private individuals, common traits also associated with Capitalism include democracy and pluralism but this is not always the case.
Capitalism has been a system of socio-political organisation throughout the vast span of history, to the extent that many would argue it is humanities default state. As has already been mentioned Capitalism when run from a laissez faire position, combined with democracy and toleration is largely regarded as the ideal at least in Western societies.
There are many benefits to capitalism, primarily the system is more productive, innovative and incentivises hard work. Furthermore it allows for a greater degree of personal freedom and tolerance (Marxism for example decrying Religion as ‘The oppiate of the masses’ is an example of the ideologies intolerance).
But it is also necessary to consider the many failings of Capitalism, largely that it is an uncaring ideology. Those who cannot compete, cannot contribute and even some of those who do find themselves in pitiful conditions. Capitalism is a heavily biased ideology favouring a fortunate few over the large majority of people. It is important to remember that Socialism and Marxism both developed from a resentment for Capitalism and how it allowed for the abuse of the masses by the upper class elite.
From this we can conclude that both ideologies have flaws, but that it also impossible to make a balanced assessment because whilst we have Capitalist societies we have no true Communist societies nor have we ever had any. From this fact alone however, many have claimed the inherent superiority of Capitalism. But if we conduct our comparison from an imperial standpoint this is like comparing an existing machine to a theoretical one, i.e. it is impossible to determine which of the machines is the better until the hypothetical one has been created. One might then argue that we could make an ideological comparison in place of practical one, whilst this is somewhat true this idea too is flawed. The preeminent issue here is defining Capitalist Ideology, there are innumerable variations of Capitalism present both in our modern world and throughout history, so against which of these do we compare Communism?