As carbon ions, at therapeutic energies, penetrate tissue, they undergo inelastic nuclear reactions and give rise to significant yields of secondary fragment fluences. Therefore, an accurate prediction of these fluences resulting from the primary carbon interactions is necessary in the patient's body in order to precisely simulate the spatial dose distribution and the resulting biological effect. In this paper, the performance of nuclear fragmentation models of the Monte Carlo transport codes, FLUKA and GEANT4, in tissue-like media and for an energy regime relevant for therapeutic carbon ions is investigated. The ability of these Monte Carlo codes to reproduce experimental data of charge-changing cross sections and integral and differential yields of secondary charged fragments is evaluated. For the fragment yields, the main focus is on the consideration of experimental approximations and uncertainties such as the energy measurement by time-of-flight. For GEANT4, the hadronic models G4BinaryLightIonReaction and G4QMD are benchmarked together with some recently enhanced de-excitation models. For non-differential quantities, discrepancies of some tens of percent are found for both codes. For differential quantities, even larger deviations are found. Implications of these findings for the therapeutic use of carbon ions are discussed.