What conflicts might arise between supporters of capitalism and socialism

To analyze the conflict first look at the way both of these systems work. Capitalism refers to a system of economy where the Government rules over as opposed to the Socialism where in the system things are owned by the public or government but ruled over by the community. This makes the conflict clear that in Capitalism the principle I that each person for Himself whiles in Socialism it is not, it is for the betterment of the Community. Both have different approaches. 

is there a year set? the question is incomplete