By default, each copied assembly has the same coordinates as the original assembly. This is expected when copying an assembly or a list of assemblys to a different layer. However, when each new assembly is in the same layer as the original assembly (for a list of assemblys, the Local option in the Layer menu), a small shift helps to separate the new assemblys from the original ones.
All other properties are the same for copied and original assemblys (only the identification numbers are different).