The difference is very likely to be that the color and or clarity grade on the EGL document is somewhat higher than the diamond would have gotten from the GIA. The stone could be a superb value even if it is not graded quite to GIA specs.
The fact is that such a price as you are being quoted would be excellent even for a J SI2 princess 1.50ct diamond. So, the judgment seems to me that the price is great and if you approve of the stone, no problem..... It sounds hard to improve the value. Just be prepared that the grading may not fit quite right. This does not change the diamond, so it only matters to some people, not everyone.