I find that I often get the same answers using both Eastern & Western astrologies.  I think they must both be correct, just a different way to get to the same answer.

My partner is a professional astrologer who does readings in both systems.  However, in order to truly understand Chinese astrology, you have to look much deeper than they year of birth, or even the hour. In fact many true Chinese practitioners actually doubt whether or not western minds are capable of grasping the intricacies of their system...it is a shame when people make assumptions about the chinese system when they are not very educated in it.  It is very profound system.

For me:

Western: Virgo
Chinese: Fire Dragon

I'm Virgo rising and Capricorn moon.  I have 4 planets in Libra, one of which is Mars (I can't remember the other three).

Am I not supposed to even exist?  How does a triple earth sign Virgo also end up being a Fire Dragon?

Like matter and anti-matter, am I supposed to just cancel myself out?

There is more to Chinese astrology then year sign. Year sign is very general basicly like your sun sign. As you know, there is moon sign and rising signs and all other planet signs that need to be taken into account. This is for Chinese astrology as well  because you have  a sign for your year, your month, your day, and also your hour of birth. Chinese actually goes deeper and i personally have not ventured that far in.  My western sign is Taurus and Chinese Metal Horse... contradictory. But there are other similarities such as my moon sign Leo and my day sign in Chinese is Fire Rabbit and hour sign is Fire Goat. So somewhere along the way things do add up. O ya and you have to take into account the elements. Alot to look at!!

The Chinese astrology discussed here is as a single system.
In fact, the prediction of destiny based on one's birth time incorporates many kinds of Chinese prediction style.

The most famous one is "Ba-zi", which transforms your birth time to eight Chinese single words to predict your destiny.
The second one is "Zi-Wei-Do-Shu", which is like Western astrology but use different set of stars.
The next one is "Chi-Zhen-Si-Yu" that is from Western Classical astrology but combined the Chinese concepts of elements, such as fire, water...

Some systems are used by minor people but worth mentioning.
"I-Ching Ba-Zi" is like its name, tranformming your Ba-zi symbols to I-Ching symbols.
"Sing-Pan" is like astrology but not uses real stars.

But if you ask me what to learn, I advise you to learn Western astrology.
There are two primary reasons: 1. Most classical writings are not translated. 2. There are too many diffient opinions that confuse biginners.

Sorry for my poor English and I am from Taiwan.
Hope the brief introduction can make you know Chinese astrology more.