Ann: SpaceLink Selected for International Space Station Demo, page-14

I will give you my best shot at an answer. I am not a scientist.

Your right, they work by being in contact with each other to form a constant connection, depending on the height of the orbit in LEO determines the number of satellites required. Because they are closer to Earth, the speed of the connection is faster than communicating with MEO or GEO satellites. These satellites can have the ability to communicate with each other with laser, I think this is still in the experimental stage and not in use at the present.

What EOS has that no one else has, or I suspect will for a long time, is the ability to not only connect with conventional methods, but also the ability to connect with the Earth via Optics. As I am sure you know, MEO satellite links with the Earth using optics are going to much much faster then conventional links with LEO satellites, also, the bandwidth is much greater, as per this announcement, 10 Gigabits per second.