If you want to collect X-rays on your SEM or TEM you have the choice of using an energy dispersive spectrometer (EDS) or a wavelength dispersive spectrometer (WDS). Which is better? That depends on what you want to do with it.

WDS is much more sensitive and has much higher resolution than EDS. Sensitivity means that WDS has a much lower minimum detection limit for trace elements. WDS can be up to several orders of magnitude more sensitive. This does not mean it is more accurate. Accuracy of analysis can be just as good for EDS as with WDS if the analyst takes the same care in sample prep, data gathering, and standardizing. Sensitivity simply means that WDS can detect much smaller amounts of a particular element than EDS. Why? Because the superior resolution provides much better signal to noise ratio than with EDS. Noise, in this case, is mostly contributed by background radiation from the sample. Because of its superior resolution, WDS can also resolve peak overlaps.