Jim explained it very well. I took an EGL certified diamond to be independently appraised, and looked at it myself through the microscope, and compared it to the gemologists control diamonds. it was graded very loosely. also, I heard EGL and GIA have different approaches to grading a diamond if it's on the fence, i.e. if color is borderline F or G, EGL will always go F, and GIA will always go G. ( but typically EGL would probably even give that one an E) And a GIA - SI2 will probably fall as a VS1 EGL.
no, your insurance company won't care, for me it was piece of mind.
If memory serves AGS is even more strict than GIA.