The only thing you can do with a personal house that you can't do with an apartment/FC room is gardening and displaying retainers; both are outdoor things. (Indoors, there is nothing a personal house can do that an apartment/FC room can't except hold more stuff.)

Apartment buildings have a chocobo stable outside them, as should your FC house unless it's completely dysfunctional.

Indoors, there's little more you can do that you couldn't do at an Inn. You can place crafting stations which give you an absolutely inconsequential bonus. You can access your FC's company chest if you have that housing item. Other stuff (summoning bell, crystal bell, orchestrion, armoire, unending journey) are all available at Inns.

And as has been said, FC houses have a few more things people can do (workshop, airship/sub, wheels, etc.) but those permissions are typically limited to just a handful of people running the FC. Most FCs also will limit who can access the gardens. They'll typically let anyone tend/fertilize, but not harvest. And most FCs will give everyone free reign of the chocobo stables.

Stables are not required to level your chocobo (though they're useful if others in the FC train yours while you aren't using it), but they are required if you want to change its color.