The main similarity between the two systems is that both systems are based on time periods of birth, and they both have 12 symbols or signs with associated personalities and fortunes.
However, there are big differences in their origins and astrological theory.
With the Chinese zodiac, the 12 signs are derived from the ancients' musings about archetypal animals, people's personalities and fortunes, and their relationships with one another and years of birth. A myth about a celestial race was later developed to explain the Chinese zodiac sequence.
This differs from Western astrology, where the 12 zodiac signs are based on constellations' positions relative to the earth. The constellations were named according to Greek mythology and astrological theory was developed based on the stars supposed influence on human personalities and lives.
In addition, the Chinese zodiac is calculated on a year-by-year base while the Western zodiac corresponds with "months".
Read more on Differences between the Chinese Zodiac and Western Astrology.