What atomic proprty makes conductors and insulators different?

The kind of bonding between the atoms make the difference that make a material conductor or insulator.

Metals form metallic bonds. The metallic bonds permit the electrons flow freely around all the material and this make the current flow. The metallic atoms have the last shell (the valence shell) relatively empty (this is with one or two electrons generally) and so the electrons flow eassily among the atoms.

That is why metals are good conductors of electricity.

On the other hand, non metal compounds are generally molecules formed by covalent bonds. These molecules do not permit the flow of electrons and so they are not contuctors but insulators.

The atomic property that distinguish between conductors and insulators is movement of the electrovalent electrons. The atoms of conductors have loosely bound electrovalent electrons which are free to move about the material, thus they are able to conduct electricity while the atoms of insulators have high resistance to the flow of electricity through them. Atoms of insulators resist the flow of charge through them.