It depends on what you define as "the Persian religion" and what you define as "the Greek religion".
Persian Religion: Islam | Greek Religion: Ancient Greek Mythology
There are no similarities between Persian main religion (Islam religion) and the old Greek religion.
Persian Religion: Islam | Greek Religion: Greek Orthodox Christianity
However, the current main Greek religion is Christianity. Refer to question below for the similarities between Islam and Christianity.
The main similarities are:
Persian Religion: Zoroastrianism | Greek Religion: Ancient Greek Mythology
Zoroastrianism and Greek Mythology have very few similarities, like multiple gods and demigods and a belief in prophecy.
Persian Religion: Zoroastrianism | Greek Religion: Greek Orthodox Christianity
Zoroastrianism and Greek Orthodoxy have very few similarities, like worship of a single powerful god (even though Zoroastrians accept the existence of other gods - monolatry), the use of icons in veneration of holy men, the concept of prophets, the concept of an apocalypse, religious-nationalism, and ideas concerning heaven and hell as well as a powerful demon who rules hell.
Currently, most Persians (or Iranians) are Muslim.
There were basically the same gods and goddesses. Like Hercules and Heracles. But their way of living was a bit different.
Catholic religion and Greek Christianity are somewhat similar, but other Greek religions are not similar to the Catholic religion.
No, not really. The only 'religion' they have is greek!
The Persians had one official religion, Zoroastrianism, while the plytheistic Greeks worshipped many different gods in different ways
Cleopatra was Greek, so she followed the Greek polytheistic religion
Greek people are part of the Christian faith. Their religion is Greek Orthodox.
Yes, they are from the Greek religion.
Aphrodite is worshiped from ancient Greek religion.
Aphrodite is worshiped from ancient Greek religion.
Greek mythology which is technically a religion
Athena is a ancient Greek goddess and a part of that religion.