Nearly, but not quite. With a house you can use the housing gardening system and chocobo stable to train your chocobo.
Though if you get an apartment, then only thing you're missing out that a person with a house has, is the gardening system. With island you'll now actually be able to use those outdoor furnishings all of the seasonal events reward.
I'd actually argue that the island is better for outdoor decorating than even a large plot.