The base game of 11 barely has a story at all. It feels like an old-school MMO (naturally), where it just drops you into the world and leaves you to your devices. Eventually you pick up nation quests that take you through a short and relatively unsatisfying storyline (beat bad guy because he's bad. okay you beat him, gg).
But the first expansion (Rise of Zilart) is where things really pick up with more and longer cutscenes - they even going as far as to retcon/flesh out the base game's ending. The second expansion takes it even further, dealing with classic Final Fantasy tropes and enemies like Bahamut.
As for the quality of the storylines, I think both 11 and 14 are great. They actually have a lot of similarities in terms of themes and broader ideas (like the existence of beast tribes, though their purpose may differ). Sorry if I'm being too vague, but if you want to experience it yourself sometime then it's best that I remain vague. There's also the possibility that more 11 themes will make their way over to 14 so I'd rather not inadvertently spoil anything.
But if you ever do play it, keep in mind that the pace of gameplay is COMPLETELY different. Again, this is an old school MMO through and through.