Yeslower pixel density/larger pixels = less noise
There is another difference, but it is probably too subjective to be mentioned by most reviewers. In a nutshell, those who own both FF and Crop sensor cameras often mention that their FF images are subjectively superior, with more "pop", which I interpret to mean better (a) contrast, (b) per-pixel sharpness, (c) detail, and (d) tonal range or shades of a color.
A rough analogy might be between mass-market sound systems and audiophile-grade sound systems. Both play the same music (i.e. capture the same light), but the audiophile sound systems are over-engineered to eliminate internal sources of noise, increase dynamic range, and improve transient response.
Some people will not hear the difference, but others will.
Among other differences, with a full frame sensor, you can get more shallow depth of field for a given focal length and aperture.
Note that depth of field is the same at the same real focal length and aperture on any camera.
Note quite true. Depth of field is derived from: the lens focal length, the aperture, the distance from the subject, and the circle of the confusion. The last item is based on the sensor size. All Canon 1.6x cameras have the same CoC; all Nikon, Sony, etc. 1.5x cameras have a common CoC; and all full-frame 35mm cameras have another CoC in common with each other. The larger the CoC, the shallower the depth of field, provided all other variables are the same. The larger the sensor (or film), the larger the CoC.
Aside from the cropping of 1.5x of the APS-C and 1.3 on the APS-H, what other differences are there?
lower pixel density/larger pixels = less noise