Raman is light scattering due to a change in polarizability;

FTIR is light absorption due to a change in the dipole moment.

If you were interested in looking at bond vibrations, for example, the symmetry of the molecule would determine whether certain modes are active in Raman, FTIR, or both techniques.  Thus using either Raman or FTIR will give you different information regarding your system.

The main difference between the two is fluorescence. In Raman -If the material shows high fluorescence, then Raman peaks are overlapped by the intense stray radiation/light, and one can't able to see representative Raman peaks from the material. In that case, FT- Infrared Raman is the possible solution, to conduct Raman, near to the infrared region wavelengths.

The other important difference is that FTIR is used to identify the nano- and micro-functional groups and bonds attached to the surface/near surface of the material. Different functional groups/bonds represent a specific wavenumbers range in an FTIR spectra. Information on nano/micro functionalised groups from the near surface would be a difficult task in Raman. 

Raman is light scattering due to a change in polarizability;

FTIR is light absorption due to a change in the dipole moment.

If you were interested in looking at bond vibrations, for example, the symmetry of the molecule would determine whether certain modes are active in Raman, FTIR, or both techniques.  Thus using either Raman or FTIR will give you different information regarding your system.

Yes, I do agree with what Ralston said. 

"FTIR" is more a working principle of a spectrometer. There are RAMAN instruments working on  Fourier transform ("FT" in "FTIR") spectrometers.

I therefore think (as Walter does) that your question is about IR absorption (by whatever type of instrument) versus Raman scattering. Both techniques are sensitive to characteristic vibrational features and electronic excitations in case they exist in the available spectral range.

As Walter wrote, in molecules and crystalline solids, vibrational modes are either Raman active or IR absorption active (or none of both, so-called "silent modes"; I disagree with Walter in so far as that typically, modes are not both IR and Raman active), depending on their symmetry character. The information you will be able to gather is complementary, therefore. 

In materials science, one is often interested in fingerprint like spectral signatures. Whether its the Raman or the IR signatures which you learn more from will depend on the specific system. A potential advantage with Raman spectroscopy might be the fact that in principle you have more degrees of freedom in choosing the experimental setting, in terms of (i) laser frequency (->sensitivity, resonances), (ii) scattering geometry, (iii) light polarization (of both, excitation and scattered light) and (iv) temperature (Stokes vs. anti-Stokes features).

The main difference between the two was already pointed out by Walter: in IR absorption spectroscopy, you measure at the frequency of the mode, while in Raman spectroscopy, the excitation is at much higher frequency and Stokes (or anti-Stokes) processes are visible as energy losses (or gains) in the spectrum of the scattered light with respect to the monochromatic excitation.