There are many different kinds of chin rests. Most fit into two categories: 1) chin rests that extend over the tailpiece and mount under the button; and 2) chinrests that mount on the side and do not extend over the tailpiece.
These chin rests come in many different shapes, sizes and materials, and have names such as Guarneri, Strad, Hill, Flesch, Dresden, Wittner, and Tekka. Some have a "lip" that is meant to fit the shape of the jaw, and others have a more flat appearance.
I do not "prefer" any one of these models over the others because no two people are built exactly alike, and a chin rest that is comfortable for one violinist may not be a good fit for another.If your current chin rest is uncomfortable, you might want to head to a violin shop and try a few of them. Look for a violin shop that carries several different models and will allow you to try them. Your teacher should also be able to help evaluate fit.
When violinists try many chin rests and still feel uncomfortable, it can be useful to add a layer of padding between the rest and the player's skin. The "Strad-Pad" is an example of such a protective layer, as is a cushion called the "gel rest," available by the maker over the Internet. The gel rest actually comes in several shapes, but its distinguishing feature is that it has a cushion made of a non-irritating hypoallergenic gel that fits over the wood in the rest. The company that makes the gel rest also supplies the gel toppers separately, and can make a double layered version for taller necks. The potential advantages of the gel rest are several. First, the cushioning of the gel reduces irritation to the skin from the chin rest. Second, it won't slip in hot conditions where sweating is an issue. Third, it helps the neck support the violin through friction between the neck and the gel. Finally, the cushion is more forgiving against the neck and often feels more comfortable to the player.
It is also important to recognize that the fit of the chin rest and the shoulder rest must be evaluated together, since the design of the shoulder rest influences the characteristics required in a matching chin rest that fits securely and vise versa.