In a new developers blog post, for now available only in Japanese, the Final Fantasy XIV: a Realm Reborn development team showcased the difference between the current DirectX 9 client and the new DirectX 11 one that will come with the expansion Heavensward on June 23rd.
You can see the difference below. DirectX 11 is on top and DirectX 9 is below it.
It's easily noticeable that shadows are much more dramatic in DirectX 11, and shiny surfaces now show lovely reflections.
If you're wondering how this will run on your PC, a band new benchmark will be released later this month.