The current will flow more easily through a thick wire than through a thin wire of the same material when connected to the same source.
This is due to the fact that the resistance of a wire is inversely proportional to the square of its diameter.
A thick wire has a greater diameter and hence lesser resistance making the current flow through it more easily.
On the other hand, a thin wire has smaller diameter and hence greater resistance to the flow of current through it.
The current will flow more easily through the thick wire than the thin wire.
It is because the resistance of a conductor is inversely proportional to its area of cross-section.
If the thicker the wire, the less is resistance and hence more easily the current flows.