With GC/MS, you will be able to identify your molecules by using library search (such as NIST library), which is useful for an unknown mixture of molecules. However, make sure the molecules are thermostable.
The choice GC/MS vs. LC/MS could also depends on the polarity : as a first approach, you can use GC/MS for apolar molecules (dissolved in cyclohexane, dichloromethane) and LC/MS for polar molecules (in H2O, MeOH, CH3CN). GC is usually easier to set-up than LC (easier optimization of chromatographic conditions).
for sure GC will be the best technique. In this case you can obtain separation based on boiling point of analytes (for non polar stationary phases) or for other stationary phases hugh selectivity regarding intermolecular interactions. The efficiency of GC columns used for separation is much bigger comparing to LC - you can use even 100 m. columns if needed!
The set of detectors possible to use in GC and their selectivity is also an advantage.
At end MS spectral libraries fog GC-MS contain over 6 mln. of compounds.
With GC/MS, you will be able to he identity of the constituents of the oil was established on the basis of GC retention indices, by comparing their 70 eV mass spectra with those reported in literature [6] and by computer matching with NIST & WILEY libraries, as well as. Where possible, co-injection was done with authentic standard compounds available in our laboratory. which is useful for an unknown mixture of molecules. However, make sure the molecules are thermostable.