I have come across studies which have mentioned Raman and FTIR to be complementary. So, why are some bands present in FTIR but are absent in Raman or vice-versa.
Raman is ascattering process and depends on the interaction of the incident light with the molecule's polarizability. FTIR is infrared absorption and depends on the dipole moment of the molecule. Both connect to the symmetries of the normal modes. Purely symmetric modes can only be seen in Raman and asymmetric modes only seen in IR (roughly) hence the idea of complementary nature.
In short, the two techniques are sensitive to different types of vibrations and therefore provide complementary vibrational spectra. In general, FTIR is used for the identification of functional groups of molecules while Raman works great for the identification of skeletal structures. When used together they can provide a comprehensive (almost complete) characterization of the molecular vibrations of the investigated sample.
For details on regard IR- and Raman-active vibrations I recommend the below resources:
+ Larkin, P. Infrared and Raman Spectroscopy: Principles and Spectral Interpretation, Elsevier, 2011.