Socialism in and of itself is not necessarily a big government ideal, neither is communism. Though I am guessing you are getting your knowledge of these terms from their colloquial use opposed to their philosophic origin.
"Socialists mainly share the belief that capitalism unfairly concentrates power and wealth among a small segment of society that controls capital, creates an unequal society, and does not provide equal opportunities for everyone in society. Therefore socialists advocate the creation of a society in which wealth and power are distributed more evenly based on the amount of work expended in production, although there is considerable disagreement among socialists over how and to what extent this could be achieved.
Socialism is not a concrete philosophy of fixed doctrine and program; its branches advocate a degree of social interventionism and economic rationalization, sometimes opposing each other." (wikipedia)
What you are talking about is authoritarian socialism (the dictatorship of the proletariat) which, in my view, is not socialism despite the name, evident in its implementation. Far from creating a free society the USSR was an extremely oppressive bureaucratic structure that hampered the development of a more egalitarian society (Even under Marx's theories, this dictatorship was only meant to be temporary).