I assume you mean, "On which side would electrical contacts to the foil have lower resistance?" The conductivity is through the bulk of the material (ignoring high-frequency skin effects, etc).
You would get better contact to the shiny side. The shiny side is shiny because it is smooth. The not-so-shiny side will be found to be much rougher at the microscopic level. This also affects the surface area at the microscopic level and, as a result, the amount of oxide that spontaneously forms. Even if your contacts have enough pressure to "squish out" the roughness, that oxide will still get in the way and degrade the contact conductivity.
The oxide layer on aluminium is notorious for interfering with electrical contacts, shinny side or not. Aluminium is sometimes a poor conductor choice for this reason. OTOH it is cheap, lightweight, and a good conductor, so it is often worth the trouble.