There are a few factors that come into play to determine the size of the exit wound. First would be bullet construction and second would be the resistance the bullet met while traveling through the animal. There are a couple other factors but I'll stick to these two for now.

A hard cast bullet through soft tissue will most likely make the same size hole going out as going it did going in. If it has to penetrate through thick muscle or bone then the exit hole will be larger as the bullet will be deformed by the time it exits the animal..

A soft point, hollow tip or ballistic tip bullet or any other bullet designed to expand with little resistance will produce a larger exit hole, These types of bullets are meant to expand so as to cause greater destruction and wound cavity to maximize their effectiveness.

Some other points were brought up by other members regarding certain anomalies that can occur with skin stretch and so forth. This has a lot to do with velocity (another factor) but they have been well covered and not as important as the points I listed so I'll leave it at that.

bullet construction and the amount of resistance are the two main factors for exit hole size