Hi Jessi,
This is a very good question, and I'm not entirely sure how to best answer it. There may be a number of reasons why the aurora in the northern and southern hemispheres are different. I hope that my answer makes sense to you!
You may have learned in school that the seasons are caused by the tilt of the Earth's rotation axis. Because of this, the seasons are opposite in the northern and southern hemispheres. When it is fall in the United States, it is spring in Australia. When it is summer in the United States, it is winter in Australia. For people who live above the Arctic Circle (near the North Pole) or on Antarctica (near the South Pole), the tilt of the Earth's rotation axis has a dramatic effect on the amount of daylight you see during different times of the year. When it is winter, people close to the poles see very little daylight and on some days the Sun may never get very high above the horizon. When it is summer, people close to the poles have a very long day indeed, and may notice that on some days the Sun never really sets. The aurora are not very bright compared to the light from the Sun, so when the Sun is up for 24 hours a day during summer at the North Pole regions, you can't see the aurora at all. Half a year later, this will be the situation at the South Pole. However, this does not mean that the physical processes that cause the aurora are not happening. The complicated interactions between the Earth's magnetosphere and the solar wind responsible for the aurora are going on all of the time - you just can't see the evidence for this with your eyes during the daytime.
There is another more subtle effect on the aurora related to the seasons and the amount of sunlight that falls on the Earth's atmosphere near the poles. The amount of sunlight reaching the Earth's atmosphere can actually cause the properties of a layer of the Earth's upper atmosphere, called the ionosphere, to vary dramatically with the seasons. Some of the differences between the aurora near the North and South Poles may be due to the fact that they North and South Poles have opposite seasons and receive different amounts of solar radiation throughout the year. This causes the properties of the ionosphere and the aurora to vary in a systematic manner with the seasons in each hemisphere.
For a long time, scientists also believed that the aurora were "conjugate," which means they thought the aurora had identical features in the northern and southern hemispheres. Now that we have images from space showing the aurora in both hemispheres simultaneously, we know that this is not entirely true. The differences in the structure and shape of the aurora in the northern and southern hemispheres may be related to the direction of the solar wind magnetic field, but scientists don't completely understand this yet.
Kris