What do Zoroastrianism and Christianity both have in common?

Answer 1

Since the two groups lived side by side in Babylonia, there may have been some borrowing in language or other minor matters. But in terms of beliefs, the two are quite different.Judaism, according to tradition, has always been monotheistic. Even at the height of the unfortunate spread of idolatry among the less-loyal Ten Tribes, there were thousands who remained loyal to God (1 Kings 19:18).

http://judaism.answers.com/jewish-history/judaism-and-monotheism

The Zoroastrians, however, believed in two gods, not one. The Jewish Sages who redacted the Talmud in the early centuries of the Common Era lived in Babylonia, witnessed the practices of the Zoroastrians, and recorded this fact (Talmud, Sanhedrin 39a). In any case, Zoroastrianism is unlike Judaism in that:

• its deity is not immanent
• it believes in worship through intermediaries, who are themselves "worthy of worship"
• evil has its own creator, Angra Mainyu or Ahriman, which had always existed
• some of its adherents believe in a self-creating universe
• some modern scholars see it as a form of pantheism
• it has "fire-temples," with worship in the presence of flame
• its adherents are not required to marry within their faith
• some Zoroastrians dispose of their dead through ritual exposure to the open sky, while some others cremate the dead body
• dogs are considered sacred
• such creatures as snakes, ants and flies were "not created by the creator of good"
• it includes a virgin birth, in which its messiah will be conceived without sexual penetration

Answer 2

They both believe we are in a Spiritual Battle between the Powers of Good and Evil.