There are two big attractions in moving from a crop-sensor camera to a full-frame system. First, depth of field is more dependent on actual focal length, rather than the ‘effective’ focal length with a crop factor applied. The upshot is that you can get a tighter depth of field to blur backgrounds and make the main part of a scene stand out; ideal for portraiture and still-lifes.
The second bonus is that, if you stick to a modest megapixel count, the photosites (equating to pixels) on a full-frame image sensor are likely to be significantly larger than those on an APS-C or Micro Four Thirds sensor. This greater light-gathering potential generally equates to much cleaner image quality and far less image noise when you need to bump up your ISO. You also get greater retention of fine detail and texture, as there’s less need for the image processor to smooth out the appearance of image noise.