PIXE achieves higher sensitivity with lower detection limits, making it ideal for detecting trace elements at ppm levels, though it offers moderate resolution, which can limit peak distinction for closely spaced elements. In contrast, EDS provides better resolution, especially with silicon drift detectors (SDD), enabling it to resolve closely spaced elemental peaks more effectively, but its detection limit is higher, typically around 0.1-1% by weight, making it less sensitive to trace elements.

What Alireza writes above is correct. Generally, the detection limit refers to sensitivity, asking what is the minimum amount of some signal to be found statistically significant above background level but does not ask where the signal comes from. Resolution refers to the ability to separate two signals in either space (spatial resolution) or energy or wavelength (spectral resolution). Often, sensitivity, specifity and resolution compete which each other, so no method can excel in all.