Easier background control in almost every situation where you want shallow depth of field, or subject/background isolation, using traditional lenses at traditional distances at traditional apertures. With an FX camera, you can use an 85mm lens to shoot a standing couple from about 20 feet away, and to throw the backdrop of of focus; with a 1.5x camera, you need to stand roughly 32 feet away for the same angle of view, and at that increased distance,using the same focal length of 85mm, the background will be MUCH,much more in-focus and sharp. Why? 1) increased camera-to-subject distance and 2) a smaller capture format.
So, there is both artistry, and science, underlying the FX versus DX situation.