If your question is about molecules instead of elements, as your original question suggested, you don't have any workaround and you have to check what the characteristic vibrations of these molecules are and the usefulness of IR and Raman may, as Pierre Caulet said correctly, behave inverse.
If you've got to choose and can have access to only one of the techniques, go for FTIR first. Its scope is still broader, has more spectral libraries for unknowns and it is more accessible than Raman, as a general rule (but there are exceptions, as with all rules...).
Dear Arvind Kaushik , both FTIR and Raman are good characterization tools you can use to identify different molecules in a sample, but as stated by Pierre Caulet and Jürgen Weippert , the applicability of these techniques would depend on the kind of molecules you want to identify and also the possible negative effects of the sample´s matrix, which could make difficult the identification process. This last issue would be more relevant in the case of Raman, since the laser source used to exciting the sample could also excite luminiscence effects from some sample´s components which could cause a strong background that would make identification more complex. These effects can affect more the Raman signal because it is usually orders of magnitude weaker than the FTIR signal.
Bear on mind, however, that new Raman instruments and appropriate set-up designs or the use of Surface Enhanced Raman Scattering (SERS) sensors can overcome most of these problems.
Thank you for adding important points to the discussion. Yes, the point of luminescence interfering with the Raman signal is crucial in deciding between the two techniques, which is nicely explained in your answer.
However, not to forget the sensitivity and application of SERS and other techniques in enhancing the Raman signal adds a lot more value to the Raman spectroscopy.