For more surface-to-surface contact problems, the source and target surfaces in a contact pair can be interchanged without much effect on the solution, the key here is to use exactly the same contact area & element size in both regions, this is the most importabt factor.
Here you are some more hints:
• The coarse surface mesh should preferably be the target, and the surface with refined mesh the source region.
• If one of the surfaces has mostly dependent degrees of freedom, it should be the target. This dependency can be due to boundary conditions, constraints or rigid elements. The surface can also be rigid if its nodes are not attached to any elements. In that case too it has to be the target.
• If one surface is significantly stiffer than the other, it should preferably be the target, unless one of the two conditions above also exist.