In XPS, X-rays are sent to the sample and ejected electrons from sample are detected. In EDX, the electrons are sent to the sample and generated X-ray photons from sample are detected.
Even though you can obtain the sample composition by both techniques (probably you talk about this information when you say "same output"), nevertheless in XPS, the main signal comes from the surface (a few atomic layer at surface, say a few nanometer) due to the escape depth of electrons. In EDX, this depth is around µm. In XPS, you can get other information like chemical state of atoms at the surface....
Atilla has provided you with an excellent and concise description of the difference between EDAX and XPS in terms of the relative "depth of analysis" of the two techniques.
EDAX effectively gives you the "bulk" concentration of elements present in a sample, but very little information about the speciation or oxidation state of each element. The chemical composition of a sample determined by quantitative EDAX measurements is generally very similar to that determined using other bulk sampling techniques such as XRF, ICP or AAS.
XPS on the other hand gives you the near surface region chemical composition of your sample (i.e. the elements present in the top few nm of your sample). It is therefore very useful in heterogeneous catalysis, adsorption, corrosion and adhesion where you only want to study processes that occur in the top few atom layers of materials (processes that EDAX would provide little to no information about). XPS analyses can also tell you the oxidation state of each element (from Li to U) from the binding energies of particular core levels, which has practical importance in many areas.
A good sample to illustrate the difference between the two techniques is a piece of aluminium foil. By EDAX, this would appear as pure Al (with maybe a very small O signal from the passivating surface oxide layer. Let's assume 99 at.% Al and 1 at.% O). By XPS, the foil would appear to be pure Al2O3 (i.e. Al3+ with 40 at.% Al and 60 at.% O), since the aluminium oxide layer on Al is thicker than the XPS information depth of 2-3 nm. By Ar+ ion sputtering of the Al foil you can erode the oxide layer to reveal the underlying metallic Al (the XPS analysis would then show 100 at.% Al). The Al peak positions in the XPS spectrum will also shift to lower binding energy on removing the Al2O3 overlayer and exposing the Al metal (Al 2p binding energies for Al2O3 and Al metal are 74.0 eV and 72.8 eV, respectively).
Thus XPS and EDAX provide complementary information about a sample, though frequently quite distinct information due to differences between surface and bulk chemical compositions.
We can extend this answer a little. EDS is an elemental analysis tool meaning it can only identify elements present. Therefore, compound analysis (iron oxides resulting from corrosion or high temperature oxides resulting during welding or quench cracking) cannot be positively identified analytically. Yes, compound standards can be collected and used qualitatively with EDS, but that is quite an undertaking. To my knowledge, XPS provides binding energy and can, therefore, identify compounds analytically and directly. Here is an example of iron oxide compounds analytically determined by binding energy with XPS: https://xpssimplified.com/elements/iron.php
In XPS, X-rays are sent to the sample and ejected electrons from sample are detected. In EDX, the electrons are sent to the sample and generated X-ray photons from sample are detected
EDX/EDS measures X-rays emitted from a sample, while XPS measures photoelectrons emitted from a sample. They are somewhat related. "Energy-dispersive X-ray spectroscopy (EDS or EDX) is an analytical technique used for the elemental analysis or chemical characterization of a sample."
Both methods are surface science tools. EDS is a tool used with an SEM used for interrogating the elemental composition. XPS is a stand alone tool that provides elemental compound composition.
EDS is a semi-quantitative auxiliary tool linked to an scanning electron microscope that provides elemental analyses of the surface of a electrically-conductive, sputtered, or coated surface. It is not a great tool for stoichiometry or compound analysis. An electron beam of approximately 15 to 25kV is focused at a sub-micron-scale spot size on the surface of material. This generates a sub-surface excitation volume of approximately 1 micron deep. Individual X-rays are emitted from the excitation volume. A portion of the x-rays are collected and their energy is measured by an x-ray detector installed in the SEM vacuum chamber. Based on the individual energies of each x-ray particle, it is possible to know from what element they came. The information is portrayed as a spectra pf measured energy in keV v. x-ray counts. Individual peaks represent the surface's individual elements semi-quantitatively without compound analyses. A quantitative elemental analysis is provided by destructive OES, but a larger sample is need
An XPS analyzer, on the other hand, is a stand-alone device with the opposite arrangement. It has an x-ray source and an electron detector. It measures emitted electrons of a surface excitation volume similar to EDS. However, data is displayed on a plot of binding energy eV v. electron counts. It surpasses EDS in one sense in that it gives elemental bonding information in addition to elemental analyses, and thereby allows for compound analyses. Again, this is a semi-quantitative tool. A quantitative compound analysis is given by XRD but larger sample is needed.
EDS is an elemental analysis tool means, it can only identify elements present on the material. While, XPS provides binding energy and can, therefore, identify compounds of elements analytically and directly.
Simply, EDS/EDX can give you detail about elemental composition of the sample while XPS can give you a detailed response about oxidation states of the samples with different binding energies just like for Si weather its +1,+2,+3,+4 and also the %age of each state. Muhammad Muzammal Hussain
EDS detects the elemental composition from a specific point of a surface and it provides only elemental composition information. On the other hand, XPS is used to detect the existing elements on the whole surface of the object. In addition to this, it determines the elements using their binding energies. So, from the data of chemical binding energy of them, you can perceive the chemical state of the compounds as well. Hopefully, you will be benefited.