Rabbit and Rooster compatibility
Rabbit (Mao, 卯) and Rooster (You, 酉): a clash (Chong, 冲).
These are fixed relations among the twelve branches of the Chinese calendar, set out in the classic San Ming Tong Hui (三命通会), written in 1578, quoted below. They describe the signs, not two people: no classic gives a method for matching two people by their signs, so there is no score here.
What the book says
Clash (Chong, 冲)
Rabbit and Rooster sit directly opposite each other on the circle of twelve, six signs apart. The book calls clashes broadly ill, and then names the ones that are not.
Among the branches the seventh along is the clash, just as among the stems the seventh along is the killing force.
地支取七位为冲，犹天干取七位为煞之义。
A clash is the twelve branches at war, striking at each other, and broadly it is ill. Yet some clashes bring the greatest blessing: those where the two sides also feed each other.
相冲者，十二支战击之神，大概为凶。然有为福之甚者，乃冲处相生。
So a clash or a break can be good or bad. They cannot be judged wholesale.
可见冲破有吉有凶，不可概论。
San Ming Tong Hui, volume 2: On the clash (论冲击) · source text
Their elements
The Rabbit is Wood and the Rooster is Metal: Metal controls Wood.
San Ming Tong Hui’s section on the zodiac animals happens to name these two. It gives the element reasoning, and then asks why the real animals do not behave that way:
Yet the Horse is the horse and the Rat the rat, the Rooster the rooster and the Rabbit the rabbit. If Water overcomes Fire, why does the rat not chase the horse? If Metal overcomes Wood, why does the rooster not peck the rabbit?
午，马也，子，鼠也，酉，鸡也，卯，兔也，水胜火，鼠何不逐马？金胜木，鸡何不啄兔？
Matched by how their elements overcome each other, the creatures of the twelve branches do not correspond at all. Wherever blooded creatures master one another, even to eating one another, it comes down to sharp or blunt teeth and strong or weak sinews.
十二辰之禽以气性相克则尤不相应。大凡含血之虫相服，至于相啖食者，以齿牙钝利、筋力优劣自相胜服也。
San Ming Tong Hui, volume 2: On the animals of the branches (论地支属相) · source text
How much it counts
A sign is one character of the eight in a BaZi chart, the year’s branch. The book reads these relations between the pillars of one chart, and tells the reader to look at the whole chart’s elements first:
Clash and break, three harmony and six harmony: where a chart has them, ask next how its five elements get on. Misfortune may give rise to blessing, and blessing to misfortune.
相冲相破，三合六合，命中有之，即求五行相得何如。或祸中生福，福中生祸
San Ming Tong Hui, volume 3: On the symbolic stars as a whole (总论诸神煞) · source text
Birth years, and 2027
- Rabbit: 1927, 1939, 1951, 1963, 1975, 1987, 1999, 2011, 2023. In 2027, the Year of the Fire Goat (Ding Wei, 丁未), the Rabbit is in harmony with the year (San He, 三合).
- Rooster: 1933, 1945, 1957, 1969, 1981, 1993, 2005, 2017. In 2027, the Year of the Fire Goat (Ding Wei, 丁未), the Rooster has no clash with the year.
A sign’s year is usually counted from Chinese New Year, between late January and mid-February; BaZi counts it from the Start of Spring, about 4 February. Born in January or early February? You may be the sign before: the sign pages check your date.
Two real people?
Each person’s chart has eight characters, and the same relations run between all of them, not only the two signs. The two-chart page sets both charts side by side, branch by branch, and gives what each chart says about marriage on its own. No score there either.
Rabbit with the other signs: Rat · Ox · Tiger · Rabbit · Dragon · Snake · Horse · Goat · Monkey · Dog · Pig.
Rooster with the other signs: Rat · Ox · Tiger · Dragon · Snake · Horse · Goat · Monkey · Rooster · Dog · Pig.