Effect of anisotropy on electrical conductivity of crystalline solids
There are indeed compounds with very different conductivity in different directions
Depending on the structure of the crystal, it is possible that a compound has very different properties in different directions. Some crystal structures cannot show this as they are essentially the same in all spatial directions, but others can. Metals don't usually have anisotropic conductivity due to the nature of the conduction bands but other conductors can show it.
The archetypal compound that shows this property is graphite. Graphite consists of multiple flat layers of covalently bonded C-6 hexagons in an extended plane stacked on top of each other by much weaker forces. The delocalised electrons in the plane can conduct electricity well but there is little scope for electrons to move freely perpendicular to the plane. So the conductivity is about 1,000 times higher along the plane than it is perpendicular to it (see Electrical conductivity of graphite).
So it is certainly possible that electrical conductivity can be different in different crystal directions. But this requires particular structural features. Other forms of anisotropy are far more common (like birefringence).