In terms of chemistry zinc is a more electro positive metal than Iron, Copper is less electropositive so , all things being equal, the zinc spray should protect the iron in steel better from rusting. According to these links- copper is less electropositive than Iron so may actually promote corrosion in steel, as does Nickel and chrome according to the last link! (Although it gets more complicated when looking at the electropositivity and relative rates of corrosion of alloys versus pure metal elements.
"Galvanic action, whether induced by the characteristics of the corroding metal itself or by contact between dissimilar metals, is caused by differences in electrical potentials, or, in other words, and for our purpose more descriptive words, by differences in solution pressures. If two metals are in contact with each other and with an electrolyte, the one with the higher solution pressure will dissolve, and is said to be electro-positive to the other metal, which has the lower solution pressure and which does not dissolve. If a piece of iron and a piece of copper are placed in contact with each other in dilute sulphuric acid, the iron dissolves and the copper remains unattacked. Replace the copper by zinc and in this case the iron is unattacked whilst the zinc dissolves. The zinc, therefore, is electro-positive to the iron and similarly the iron is electro-positive to the copper, and in the electrolyte the direction of the galvanic current will be respectively from the iron to the copper and from the zinc to the iron, that is, from the more electro-positive metal to the less electro-positive metal. It is clear, then, that the more electro-positive component of such couples functions anodically, and conversely it may be correctly inferred that whenever a metal functions cathodically it does not corrode."
I would stick with Zinc because if the zinc coating is breached the zinc will still provide some protection to the steel wheras copper may promote corrosion.
Copper is a much better conductor than steel or zinc so that may be why it is used in some weld thru sprays.