I don't believe there is any particular reason other than choice of design by the manufacturer. While Ade is correct in that you can date them based on design however you would have to know who the maker is as well as have a knowledge of or reference to the different design changes.
However as a whole, I've seen examples of pre Spanish American War EGA's with and without the rope as well as recent examples with and without the rope.
Collecting EGA's is a hobby in its self and potentially an expensive one depending on the rarity of design, maker and its age.
One thing you can do, however, is distinguish between an Officer and EM/NCO EGA. For an officer, the area between the eagles legs are hollowed out whereas an EM/NCO's example would be a solid piece (similar to the examples on the uniforms I posted).