The Replace all selected objects' labels option copies over the label reset information, but the copy highlighted labels option currently does not. This is probably because it is more ambiguous what a user would actually want to have happen. In the Replace All case we know that the user wants the other objects to exactly mimic the label situation of the highlighted object. However, with the Copy option the user is hand picking a subset of the labels they want to copy over and that will be added to the existing labels on the other objects, which makes it less clear.
If you feel like this is an important, and unambiguous, feature feel free to post a new idea or email dev@flexsim.com.
Matthew Gillespie
FlexSim Software Developer