Vibrational spectroscopies (IR and Raman) allow to estimate the ratio between free and esterified FA (very important in the quality of oils), the unsaturation degree and the ratio between cis and trans isomers. It is also possible to discriminate some of the major component of oils, i.e. distiguish oleic from linoleic acid. These techniques are non destructive and are quite fast.
From the quantitative analytical chemical viewpoint, especially operating at low concentration limits of detection - Neither of both the mentioned methods!
The core analytical methods for lipidomics, in general, are MS-based ones such as GC–MS, HPLC–ESI (or APCI)-MS/MS.
You can read for example, the followig paper, where nevertheless that we have performed quantitation of low molecular weight analytes in oils by MALDI, we have a representative introduction part comparing the hybrid MS-methods towards their time, labour and cost consumption for analysis of lipids. So that, you may find useful info among the reference part as it has been shown:
[1] Journal of Food Measurement and Characterization, 2014, 8, 15-28, Simultaneous quantitation of naturally occurring insecticides, acaricides, and piscicides in rapeseed oil by UV-MALDI mass spectrometry, Bojidarka Ivanova,Michael Spiteller