Very briefly: both give information on the vibrational modes of molecules described by the same force constants. The selection rules and the band intensities are different: in Raman spectrscopy the transitional polarizability should be different from zero, in IR the transitional dipole moment. The advantage of Raman is that it can be performed in aqueus solutions (althoughit is possible with IR if you use ATR with non-water soluble ATR crystals). the disadvantage of Raman is the it cannot be well measured in case of fluorescence (that can be avoided by using more laser sources).
Very briefly: both give information on the vibrational modes of molecules described by the same force constants. The selection rules and the band intensities are different: in Raman spectrscopy the transitional polarizability should be different from zero, in IR the transitional dipole moment. The advantage of Raman is that it can be performed in aqueus solutions (althoughit is possible with IR if you use ATR with non-water soluble ATR crystals). the disadvantage of Raman is the it cannot be well measured in case of fluorescence (that can be avoided by using more laser sources).
I agree with Gyorgy Banhegyi. Hower one need prepare sample for IR experiment always. For RS experiment it is depends on targets (pressure, crystal orientation). We do not need special sample preparation usually. Techniques supplement each other.
The Raman spectroscopy is a very powerful tool for solid state studies especially for oxides. You can access at very low wavenumbers (close to 10 cm-1 or less). The selections rules indicates the existance of inactives vibration modes in IR. The Raman is very interesting for studies surface/interface under operando .
Raman spectoscopy is based on a second rank tensor modulation i.e. the polarisability. IR is a first rank modulation, the dipole moment. In a centrosymetric crystal RS and IR are mutually exclusive. In that case, normal modes active in RS belong to "gerade" irreducible representations, normal modes active in IR belong to "ungerade" irr. rep. Some of the modes can be inactive both in RS and IR spectoscopy.
In IR those transitions are active which beliong to the same point groups as x, y and z axes, while in Raman those, which transform as xy, yz or xz. The first means that the dipole moment of the transition should be different from zero, the second that the polarizability of the transition should be differenct from zero.
Selection rules and bands intensities are different for IR and RAMAN. at the same time, IR basically due to the absorption of light and it has change in dipole moments. On the other hands, Raman effect is due to scattering of light. The molecules need not possess a permanent dipole moments.