Term "western astrology" exists thanks to the Roman empire who implemented it thanks to the wars between the east and west in the Eastern Europe. It is, by all means, the true system that's dating to this day.
Western astrology is a slang, a term used in the ways to determine that it relays on the 12 Zodiac signs. There can't be 9 or 10, nor 13 or 15. Only 12 because of the elemental individuation on Fire, Water, Earth and Air. There're three Zodiac signs for each element.
Fire = Aries, Leo, Sagittarius
Water = Cancer, Scorpio, Pisces
Earth = Taurus, Virgo, Capricorn
Air = Gemini, Libra, Aquarius
They represent these trinities :
Fire = Space, the trinity of space itself.
Water = Energy, the trinity of energy itself
Earth = Matter, the trinity of matter itself
Air = Time, the trinity of time itself
The human body is made out of Fire (heat of body), Air (we breathe), Water (obvious) and Earth (carbon based organisms). The four elements essential for life are also there and the Zodiac itself IS BASED upon the elements rather than constellations. In fact, constellations don't exist as "bodies" in astronomy. They are just a way of human expression and realization, usually thanks to the urban legends etc.
As for the Chinese zodiac, in my experience and knowledge, it's not as accurate as the original one, however they do know a lot about numerology and the cycles of the years which is not used in the common astrological sense. They have a great knowledge about Feng Sui as well as numerology so I recommend those areas of Chinese knowledge.
Best regards.