There are as many differences between Saturn and the solar system as a whole as there are similarities. Both Saturn and the sun are orbited by a number of objects moving in (mostly) counterclockwise orbits, a remnant from the rotation of the primordial gas and dust cloud which eventually formed the solar system. Some of these objects have atmospheres, and some are relatively small objects concentrated in specific orbital zones. Saturn is even a net emitter of energy like the sun; due to its internal heat, it radiates more energy than it receives from the sun.

However, the differences include:

--Objects in the solar system show a distinct gradation in composition depending on how far from the sun they formed, with rocky and/or metallic objects close to the sun and increasing amounts of ices and frozen gases at greater distances. Objects orbiting Saturn show no such gradation, since they either formed at Saturn's distance from the sun or were subsequently captured, and their composition has nothing to do with their relative orbital distances from Saturn.

--The bulk of Saturn's rings are inside the planet's Roche limit; that is, an object of any great size would be torn apart by tidal forces. In fact, this is one theory of how Saturn's rings formed; another is that they represent leftover material from Saturn's formation that was too close to the planet to form a moon in the first place. On the other hand, the asteroid belt is beyond the sun's Roche limit, and there is no reason why a full-sized planet could not orbit the sun at those distances.

There are other differences between Saturn's rings and the asteroid belt. Saturn's rings are mostly water ice, again indicative of the planet's distance from the sun, while asteroids are mostly made of the rock and metal found closer to the sun. Because the asteroid belt is beyond the sun's Roche limit, asteroids can range up to hundreds of kilometers in diameter, while the particles in Saturn's rings range in size from dust to small boulders. Additionally, Saturn's rings are only a few meters thick, with all of the particles orbiting in the exact same plane. Asteroids, however, have a range of orbital inclinations, and the asteroid belt more closely resembles a fuzzy donut than a ring.
Source(s):
http://zebu.uoregon.edu/~js/ast121/lectures/lec20.html
http://en.wikipedia.org/wiki/Roche_limit
http://csep10.phys.utk.edu/astr161/lect/saturn/rings.html
http://www.solstation.com/stars/asteroid.htm

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