Pretty much everything opens up a bit, more dungeons, the guildhest gets more interesting, you also gain access to grand company (and making your FC I think), the materia stuff, etc.
The story quests, dungeons, bosses were a bit more interesting than running from npc to npc you typically do until you reach lvl15, but I can't really say if it actually gets better and better because beta's story mission pretty much stopped after Ifrit (which I found pretty cool), the last few dungeons I went through were also pretty decent, so it gave me impression that there will be more of them later on, but of course I could be wrong, but I hope not
Edit: I did a lot less quests after lvl15 though, so don't take "everything" too literally, lol.