To be fair, there appears to be many websites that also claim that GIA are stricter with their certification than EGL, including jewellers that have tested the two by sending diamonds to both and found differences in the results - the GIA showing lower gradings than the EGL.
The argument for charging more for a GIA stone appears to be because a GIA I colour grading, could be graded as a G with EGL. Therefore you have to look at a higher graded colour, more expensive EGL certified diamond to compare like for like. (I am using this as an example for one I have found online).
I have never sent a diamond both to GIA and EGL to get a direct comparison. I am only going off what I have read by jewellers/wholesalers who have done this. I am just trying to balance the argument put forward in the above article.