For "ideal" specimen (homogenious bulk one) results should be about the same. Error can come not with point, but with area EDS - because software (and theory) is made for point analysis. SEM-EDS systems were created for MICROanalysis.
The area EDS gives a statistical average of elemental composition over the area while point EDS gives elemental composition at the point.
The point EDS elemental composition is the same as the area EDS elemental composition. The difference between them indicates the non-ideal nature of the sample.
This really depends if your material is homogeneous. If sample is homogeneous, results should be similar. it is also presume that the sample is not layered, if it is, the results will also be affected by the acceleration voltage use.
If the sample is not homogeneous, need to consider the area that would be affected by the electron beam to generate characteristic Xray that will influence the results. The rule of thumb the depth of penetration of the sample is also same as the radius that the electron beam will reach, that will give you the results of other element is present in the area. However, this is only significant when your magnification is 10000x or above. This applies to area EDS as well. So the analyst need to know the purpose of analysis and area they are analyzing. Wrong setting will give raise to wrong results. I can only say… know your sample.