It's really simpler than it sounds or appears.
In FFXIV 1.0 we only had linkshells that served as guilds. Although as a guild system it was really bareboned. It was basically a list of people much like a friendlist but with a guildchat channel. You could join multiple linkshells and follow all their chats in the log.
FFXIV: ARR now introduces Free Company which becomes the new in a sense true Guild system. Any MMORPG usually forces people to only join 1 guild. This is what Free Company will become.
However, linkshells still remain with the same function as in FFXIV 1.0. But will serve more as a way to create social groups.
Conclusion(tl;dr)
Free Company = The true typical mmorpg guild (Join 1 and only one) and allows acces to future Guild housing
Linkshell = social groups (Join as many as you want), no additional benefits
Additional edit:
You can join a Free company and also join multiple linkshells at the same time. Just wanting to clarify it.
In FFXIV 1.0 we only had linkshells that served as guilds. Although as a guild system it was really bareboned. It was basically a list of people much like a friendlist but with a guildchat channel. You could join multiple linkshells and follow all their chats in the log.
FFXIV: ARR now introduces Free Company which becomes the new in a sense true Guild system. Any MMORPG usually forces people to only join 1 guild. This is what Free Company will become.
However, linkshells still remain with the same function as in FFXIV 1.0. But will serve more as a way to create social groups.
Conclusion(tl;dr)
Free Company = The true typical mmorpg guild (Join 1 and only one) and allows acces to future Guild housing
Linkshell = social groups (Join as many as you want), no additional benefits
Additional edit:
You can join a Free company and also join multiple linkshells at the same time. Just wanting to clarify it.