The classical feng shui schools take into consideration the feng shui compass readings and the energy of cardinal directions.
The Western, or modern schools of feng shui do not take the compass readings into consideration, which makes it easy to apply it anywhere in the same way.
So, if you are working with a modern school of feng shui that uses the BTB Bagua, the answer is easy - it makes no difference if you live in the Northern or Southern hemisphere, as the feng shui application is the same.
How do you feng shui your home, though, if you live in the Southern hemisphere and use the classical feng shui school? We'll go through it step by step. But first, let's clarify the essence of your concern for those readers that might not be familiar with this feng shui dilemma.
The bagua, or the feng shui energy map, being the foundation of feng shui work, assigns different energies to different directions. For example, North has the energy related to your career and is nourished by the water feng shui element energy. South has the essence of the fire feng shui element energy and supports your efforts in expressing your inner fire, your talents, and creativity.
If you live in the Northern hemisphere - where feng shui was developed thousands of years in China - you know you receive the Fire element/Strong Sun/Yang energy while facing the South direction. However, if you live in the Southern hemisphere, the Fire element/Strong Sun/Yang energy is coming from the North, not from the South. Shouldn't you reverse the bagua, then, so that it correctly reflects the present energies?
Different Approaches to Feng Shui
You can see now why many feng shui consultants differ in their approach; some affirm that the bagua should be applied the same way in both hemispheres, while others are suggesting a more harmonious, deeper approach to this dilemma.
This is where the understanding of feng shui as science and art is imperative because an artful approach to feng shui - based on a strong, solid knowledge - is often a wiser, deeper approach. Think of the roots of feng shui, imagine how it all started.
The ancient feng shui masters were not walking the earth with feng shui compasses in their hand. Being very wise and experienced geomancers, they knew how to read the patterns of Chi, or energy movement, as expressed in various natural phenomena. They knew which land has prosperous energy and why, and which sites must be avoided. They knew the best placement and arrangement for various spaces as defined by the desired optimum function.
Most of all, though, they knew that humans could only prosper and thrive if they live in harmony with the natural laws of the Universe, especially their immediate natural surroundings and climate. If you really connect to this energy, to a deep understanding of nature and body rhythms, you will realize this is the only true foundation for successful feng shui work.
A house that is not in harmony with its immediate environment cannot possibly nourish you. So, if you know that the strongest fire element energy comes to you from the North direction, and not from the South, then, of course, it is wise to reverse the bagua.
Here are just a couple of basic facts with a simple explanation as to why it is best to reverse the traditional bagua when applying classical feng shui in the Southern hemisphere.