What is the difference in the systems?
From where do these differences come from?
WHY are there so many different systems?
What system does EA use?
WHY does EA use that particular system?
First, the Wikipedia article on house systems looks pretty good as far as listing many of them and briefly addressing their differences and histories. http://en.wikipedia.org/wiki/House_%28astrology%29
As to why are there so many, like anything else in human life, people come up with the latest great idea that they think is superior to existing ideas. Some people sincerely think they have found something that is an improvement on existing methods, while others do something new trying to make a lasting name for themselves.
Jeffrey Wolf Green shared with us that he had tried all of the house systems and to him the results he found with Porphyry correlated the closest with what he was experiencing in people's Souls.
We are talking about Life, something that is real, breathing and alive, that was created with a set of rules or laws by its Creator. Thus it goes beyond someone having a new great idea. If a house system is going to be accurate it has to correlate with the natural laws of creation. Then it will produce accurate results.
Most of the house systems use a quadrant system that divides the circle into 4 quadrants. Quoting from Wikipedia
There are many systems of house division. In most the ecliptic is divided into houses and the ascendant (eastern horizon) marks the cusp, or beginning, of the first house, and the descendant (western horizon) marks the cusp of the seventh house. Many systems of house division called quadrant house systems also use the midheaven (medium coeli) as the cusp of the tenth house and the nadir (imum coeli) as the cusp of the fourth house. Some house systems divide the celestial equator and the prime vertical instead of the ecliptic. ...
Goals for a house system include ease of computation; agreement with the "quadrant" concept (ascendant on the first house cusp, nadir on the fourth, descendant on the seventh, and midheaven on the tenth); defined and meaningful behaviour in the polar regions; acceptable handling of heavenly bodies of high latitude (a distinct problem from high-latitude locations on the Earth's surface); and symbolic value. It is impossible for any system to satisfy all the criteria completely, so each one represents a different compromise. The extremely popular Placidus and Koch systems, in particular, can generate undefined results in the polar circles. Research and debate on the merits of different house systems is ongoing.
Placidus is the most commonly used system. My understanding is this is because it was the first house system with a book of tables to determine house placements. This was before computerized charts, when it was a lot of work to cast a chart. Placidus made it easier so people adopted it. Personally I haven't found its results especially accurate.
The main difference in quadrant systems is how the space within one quadrant is divided into 3. In porphry, as Linda said, the space is divided into 3 equal parts. Jeffrey felt this modeled the natural law of the Trinity that is seen throughout creation. We have cardinal, fixed, and mutable, and past - present - future. Thus 3 equally sized houses.
For myself, when I started studying astrology people were asking me "Where is your Scorpio?" because of the way I was, always seeking the bottom line and wanting to understand the Why of things. I have no planets in Scorpio in my natal chart. When I started learning EA and became aware of house systems, I discovered that in the Porphory house system my Pluto is in the last degree of the 8th house, while in most other systems it is in the 9th house. In EA, Pluto and 8th house and Scorpio correlate with the Soul. Thus with Pluto in 8th, the Soul itself is emanating its Scorpio nature. And in the last degree it means this placement is culminating within that Soul. That happened to correlate with exactly how I felt inside myself. This was not revealed in the other house systems I'd tried. Thus I received my own Scorpio proof based on my own case. Since that time I have fairly often experienced the Porphory chart shifting certain house positions in client charts that I've almost always felt made more sense than the natal chart they were used to seeing. To me this is an example of why Jeffrey recommended and used the Porphyry house system.
I think every EA student should experiment with other house systems if they feel inclined to do so, and reach their own conclusion. The reason to use Porphyry is not because someone said it was better, or the one to use, but because the astrologer has experienced that for them, it is accurate and correlates with what they find within the client whose chart they are reading. That said, for people starting with EA who don't know much about house systems, we suggest using Porphyry.