Besides mechanical differences, the primary difference between aluminum and copper in antenna construction is RF resistance. Copper will have slightly less RF resistance for the same surface area. Increasing the surface area slightly allows aluminum to exhibit the same RF resistance as copper.
RF resistance is unique due to the tendency of the RF current to crowd around the surface of the conductor. As the frequency is increased, the RF current crowds even more toward the surface, occupying an increasingly thinner layer of the metal. Because of this effect the surface area of the conductor becomes a dominant factor in determining the RF resistance and conductors can be hollow tubes since no appreciable current would flow in the core.
But specifically to your question, RF resistance has no appreciable effect on resonance or element spacing. It will potentially impact antenna efficiency and gain. This is critical in certain classes of antennas such as small loop antennas where the radiation resistance is quite low.
With typical antennas such as a yagi, the difference in efficiency and gain due to RF resistance differences between aluminum and copper will most likely be neglible. If you are concerned about your specific case, provide more details regarding the type of antenna and the intended frequency range of operation.