FC houses have access to the workshop where various housing skins, buff chargers and ship parts can be assembled. The workshop can also send airships & submersibles out on missions (essentially fancy expensive retainers, but for the fc instead of individual players). Indoor flower pots can grown seeds, outdoor garden plots and grow & crossbreed seeds. The last advantage is the ability to charge buffs. While lvl 1 & 2 buffs can be straight up purchased from the action vendors, the grade 3 buffs have to be crafted and charged, which can only be done within an fc house.

Personal houses have the same ability to grow indoors/outdoors and crossbreed outdoors as the fc houses, but lack the workshop.

Apartments/FC Rooms only have the ability to grow seeds. No crossbreeding. Apartments have an advantage over fc rooms in that there's no fc/house attachment so there's no worry about losing it if you want to switch fcs or something happens to the fc house.

Beyond that, they're just there for decorative purposes.