If these two systems could or not be compared we should first lay out some definitions.
The social system is represented by people or groups of people. It is a social structure that refers to entities or groups of people that are definitively in relation to each other by having different functions, characteristics, origin or status. A social system is comprised of interdependent set of cultural and structural elements understood as a unit. Sociology is the study of human social behavior and especially the study of the origins, organizations, institutions and development of human society.
The economic system encompasses the production, distribution or trade of goods and services and consumption by different individuals, businesses, organizations, or governments. Economy as a study deals with the production and consumption of goods and the transfer of wealth and explains how people interact within markets to get what they want or how they accomplish certain economical goals.
To understand if the systems are comparable or not we should probably dig even more and try to outline also the basic differences between socialism and capitalism.
The capitalism is a theory or an economic system in which property, investment in business and ownership of the means of production, distribution and exchange of wealth, of capital, land, etc. are owned and controlled by individuals directly or through ownership of shares in companies.
The socialism in comparison to the capitalism is an economic theory or system in which the means of production, distribution and exchange are owned by the community collectively, usually through the state. It is characterized by production for use rather than profit, by equality of individual wealth, by the absence of competitive economic activity, and usually, by governmentally determined production plan investment, prices, and production levels. Therefore, we have a planned market versus market economy as in capitalism.
The last two terms that we have to somehow define are democracy and communism. Where democracy stands for a system or a form of government in which people choose leaders by votes (typically elected representatives) of the whole population or all the eligible members of a state. And communism (from Latin communis: common or universal) is a theoretical system characterized by a classless, moneyless, and stateless social order structured upon common ownership of the means of production and by the organization of labor for the common advantage of all members.
Therefore, we definitively can compare social systems that represent human behavior, organization, relations or social structure. On the other hand we can measure up different economic systems of producing and distributing of goods and services. However, it becomes rather complicated when we discuss the bases of a socio-economical foundation (or states) most of the mankind lives and works in. Simply, one cannot compare incomparable, e.g. different economies with different social systems. They are cross incomparable.