Atom vacancies are intrinsic defects of carbon nanotubes. Using a zigzag nanotube as reference, this paper focuses on the comparison of calculations performed within density functional theory and a number of classical force fields widely used for carbon systems. The results refer to single and double vacancies and, in particular, to the induced structural changes, the formation energies, and the energy barriers relative to elementary processes such as reconstruction, migration, and coalescence. Characterization of these processes is remarkably different in the different approaches. These findings are meant to contribute to the construction of DFT-based classical schemes for carbon nanostructures.