Well my understanding is linkshells are supposed to only be a means of communication across great distances, where as companies are more of a clan or guild of like minded individuals where being a member of such clan/guild provided perks suchs as group crafting, housing, and battle content. I remember reading that there would be company content that you would use ships/airships to get to. Also companies would not have the ridiculous player cap that LS's have as well as more functions such as ranks, the ability to remove folks if need be, pretty much all the functions LS's are lacking.
It doesn't take a genius to see the difference between companies and linkshells.