I like full frame because there is less noise in the photo (especially at higher ISO levels), you get a natural vignetting in the image, a smaller depth of field and more background blur (bokeh), and a better image dynamic range. The full frame does better in low light conditions because of the larger image sensor as well. The optical viewfinder is also much larger to look through than that of a crop sensor camera.
Also, since the camera sensor is smaller in the crop bodies and mega pixel counts grow with each new camera that comes out, the camera has to do more in camera noise reduction so the photo wont look as “grainy” with a large MP number. Some argue it degrades image quality, it makes sense why it would but its hard to tell.
A full frame sensor is 24x36mm (equivalent to a 35mm film camera) and a 1.6X crop camera APS-C sensor is 15x22.5mm.