Even if you will go to different instruments (same manufacturer or even worse, different manufacturer) you likely will get different results. The question is, how do you start to define "different"? If you do want make sure what you can expect in such case, use a standard material of homogeneous composition, preferable a stochiometric phase and test it.

For steel you can use any homogenized (!) steel. Otherwise you are comparing apples and oranges, i.e. if your material is inhomogeneous the system should show this of course. If you have a homogenized steel as thin TEM sample and you compare this with a bulk measurement, the chance to find inhomogeneities in TEM is much bigger because of the differen interaction volume. For stochiometric sample in TEM you should see no differences to the bulk, but a) there are different correction terms which are based on theoretical assumptions. (b) The acquisition conditions are usually different. And (c), it might be important how did you prepare the sample. Altogether, I wouldn't be surprised about quantitative differences measured in TEM and SEM. On the other hand, often only relative changes are of interest, since the manufacturer of the steel already tells you the composition, i.e. you are expecting inhomogeneities....which are different in SEM and TEM. :-) Thus, you need to make sure what do you want to have. Your measurement systems will already show differences, and your investigation procedure as well.  

Dear Oleg,

Yes it is quite common to find different EDS/EDX results for same sample. EDS analysis  don't provide the same results in multiple measurements for the same sample unless the sample is homogeneous.  EDS  poorly detects light elements like (O,C,H,N etc.) and its quantification of C and O is usually inaccurate if adventitious sources of theses elements exist. Moreover, EDS signals are usually obtained from the upper few micrometers of the sample, i.e. it is not a bulk analysis technique.  In addition to that, correct calibration is also important.

You can check the following link for more opinions on EDS accuracy.

https://www.researchgate.net/post/What_is_the_accuracy_of_energy_dispersive_X-ray_spectroscopy_EDS_in_measuring_composition_elements_of_nanoparticles_in_weight_and_atom_percentages

Even if you will go to different instruments (same manufacturer or even worse, different manufacturer) you likely will get different results. The question is, how do you start to define "different"? If you do want make sure what you can expect in such case, use a standard material of homogeneous composition, preferable a stochiometric phase and test it.

For steel you can use any homogenized (!) steel. Otherwise you are comparing apples and oranges, i.e. if your material is inhomogeneous the system should show this of course. If you have a homogenized steel as thin TEM sample and you compare this with a bulk measurement, the chance to find inhomogeneities in TEM is much bigger because of the differen interaction volume. For stochiometric sample in TEM you should see no differences to the bulk, but a) there are different correction terms which are based on theoretical assumptions. (b) The acquisition conditions are usually different. And (c), it might be important how did you prepare the sample. Altogether, I wouldn't be surprised about quantitative differences measured in TEM and SEM. On the other hand, often only relative changes are of interest, since the manufacturer of the steel already tells you the composition, i.e. you are expecting inhomogeneities....which are different in SEM and TEM. :-) Thus, you need to make sure what do you want to have. Your measurement systems will already show differences, and your investigation procedure as well.  

The difference in composition measurement should mainly depend on your sample. TEM interaction volume is too small (thin section) compared to SEM (bulk sample). If sample is heterogeneous in submicron scale then you are comparing 2- different things and end result will be different. Steels are normally heterogeneous and you ought to expect a difference between SEM and TEM.

The other factor you should consider is elements you quantifying. C- analysis as a light element is difficult to quantify by EDS on both SEM and TEM because of the low detectability and strong matrix effects. 

Probably you could use other techniques such as XRF for bulk analysis of major elements in steel. For precise C- contents measurements, you could use combustion analysis such as C/H/N analyzer.

Dear colleagues, thank you very much for your helpful replies. You have explained me many aspects that I need to take into account when investigating my Cr-Ni stainless steel. I am interested in the denuded (depleted) zones, located in near-grain boundary regions in irradiated materials. So, basically, I am a priori interested in the inhomogeneous distribution of elements (particularly Cr and Ni) in a relatively narrow area, the factor that you all specified. A number of previous studies indicated that concentrations of the studied elements may vary significantly (up to 4wt.% at at a distance of 20nm from GBs). A literature review shows that some investigations were performed using SEM samples, while the others were based on TEM analysis. I was wondering what uncertainty each method could potentially bring to the final results. Working with irradiated TEM samples, where the swelling is relatively high, I have noticed that pores affect EDX analysis by changing dead time time for each local area of interest. There are many other important aspects which now I will try to take into account to reduce their effect on quantitative analysis. Thank you again for your opinion and advice.

TEM specimens provide better spatial resolution (because they are thin) and could be used both for TEM and SEM. You can put your TEM specimens in an SEM (preferably on a low atomic number substrate, such as carbon) and get spatial resolution close to that of TEM EDS. In this way you can better compare differences between your TEM and SEM EDS systems. You may not be able to quantify results for thin film with SEM software, but relative heights (areas) of peaks could be useful.

Vladimir, thank you very much for your advice!

Yes you may expect different result rather EDX gives you better particle size compared to other two method mentioned

The main problem in SEM-EDX is the background signal from regions close to your supposed point of analysis (due to multiple electron scattering in the thick sample, reducing both your spatial resolution and your chemical sensitivity). The phi-rho-z method is probably the best to cope with absorption and should correct this properly. The main problem  in TEM-EDX, where the spatial resolution is much better,  is a correct absorption correction because foil thickness, density and take-off angle are usually not known precisely. We have recently developed a  new method of internal absorption correction and tested this for semiconductors (J. Microscopy, vol. 260, issue 3 (2015) 427-441 and vol. 262, issue 2 (2016) 151-156), but it should also work with your steel sample where you have K and L lines from Ni and Cr ; C will remain a challenge. Please try it and let me know if you have questions!