I am not an expert, so I don't know everything, but EGL stands for European Geological Laboratory and GIA stands for Gemological Institute of America. These are two different organizations which can provide you with a report for your diamond.
Around here most people feel that the GIA provides a more accurate reoprt related to diamond color and clarity. And, that a diamond with a GIA report has a better resale value.
As for other differnces I am not sure as far as what is included on the report. I will let the experts answer that one.
You might want to do a quick search of the forum as I think that others have had this same question.
Also, don't let David catch you calling it a certificate. It is called a report..
Also, EGL has different "branches". EGL USA is supposed to be the best of the EGL branches, but thier standards of grading overall are more lenient than those of GIA. Meaning an EGL graded H si1 diamond could very well be graded a J i1 diamond by GIA. Generally, they can be a couple of grades off what GIA might grade something at. Not always I'm sure.. but as far as I can tell from reading about EGL items, that's always been the case.
Also, I believe (I could be wrong) that EGL will give an SI3 grade. GIA does not. GIA goes from SI2 to I1. They have no SI3 grade.
In my personal opinion, an EGL USA report is better than no report at all. Some of the vendores here at DT sell stones with EGL USA reports. I know I've seen those ocassionally around here.
GIA tends to have the best reputation in the industry because their grading is so strict and their reports are very accurate. They are an unbiased, nonprofit lab who provide honest and accurate reports. I would not buy a diamond if it was not GIA-certified. Hope this helps!