Well, it doesn't do anything except have more Company Seals max.

Currently the rank only increases when he adds content to the Big Company's squad. It is perhaps once by extension, useless.

Basically the GCs are to make a sort of faction vs faction vs faction, except that the PvP doesn't bring much when interesting and if I remember well, there was only one glamour set on Shadowbringer vs 2 or 3 for other extension, if you want to look like a Metal Gear Rising character...