Why would Auger electron detection have potential for higher spatial resolution than EDX
I think this is a good question. The problem is more fundamental. In both cases, you would be using electron beams on the sample.
In EDX, you are shining a beam of electrons and detecting the X-rays. Here comes the main problem. It is hard to focus the X-rays. Mea culpa here. As Jon commented it is the depth of penetration of the electron beam and the corresponding X-ray emission that main affects spatial resolution. This picture roughly tells the story:

Auger electron electron spectroscopy, you are focusing a beam of electrons and you detect electrons. It is relatively easy to focus electrons using &quot;lenses&quot;. Hence you can point point the exact origin where the electrons are being ejected.
Also, think about the depth profiling. EDX is not a surface technique unlike Auger. I used to have this misconception until I attended a workshop on surface analysis. The electrons can easily penetrate the sample and similarly originate from the some depth as well.