Since the escape depth of Auger electrons is low, it is possible to obtain the depth distribution of elements of interest by sputtering the sample with an ion gun (e.g. Ar⁺) and obtaining Auger spectra  alternately in between sputter steps. In contrast to Auger analysis, EDS analysis involves the detection and measurement of X-rays that are characteristic of the species present. The depth of escape of these X-rays is about 1um, which is more than  100 times deeper than the  Auger electron escape depth. Please note that the EDS information depth is variable, particularly with respect to the electron beam energy.

Auger analysis is generally more suitable than EDS analysis for the analysis of very thing surface layersd, particles or contaminants, e.g. 50 nm thick, or less. If EDS was used for such an analysis, it is very likely that the spectra obtained would contain more information from beneath the surface layer or feature of interest, rather than from the surface of the sample itself. This convolution of surface information with intense signal from beneath the surface makes it difficult to fully and unambiguously identify thin surface contaminants, particles or layers. As a general guideline, EDS is most suitable for measuring foreign matter and local areas of 0.5um  thickness or greater. 

When an EDS detector is mounted on a TEM device, the sample is usually sliced to a thickness of 100 nm or less for TEM measurement. Because the sample is so thin, there is just empty space in the volume where the most intense X-rays would come from in a bulk sample. Thus, TEM-EDS does not depend on the characteristic X-ray escape depth as in SEM-EDS. The thickness of the sample is effectively the information depth. This is because the thickness of the TEM sample is less than the characteristic X-ray escape depth.