The term "GIA certified diamond" is misleading. The GIA does not certify diamonds; rather, it grades them. In the jewelry business, the words "GIA certified" and "GIA cert" are often used to refer to diamonds that have completed the GIA's rigorous grading procedure, as well as the reports that accompany them.
They have the finest reputation for diamond grading accuracy. A diamond with a GIA diamond report is worth more than one graded by EGL USA. Not only when you acquire it, but also if you decide to sell it or trade it up in the future.
If you're purchasing a diamond and don't mind if the quality on the "certificate" is wrong by one or two grades, EGL USA could be alright. However, if you are more concerned with quality and want stringent grading on your diamond, you should remain with GIA.