Yeah, Tamerlane, you build mounds of thousands of skulls of your vanquished enemies and then talk about little ol’ me kicking your ass? 
The Assyrians, so-called (like Tariq ‘Aziz), are Christian Iraqi speakers of the eastern Aramaic or Syriac dialect. They have revived the name “Assyrian” in modern times to connect with the past empire of northern Mesopotamia after the name had been out of use for, oh, over 2,000 years? Their language is Semitic, closely related to both Hebrew and Arabic. In some respects it resembles Hebrew more, in other respects it resembles Arabic more. But it’s like comparing French, Italian, and Spanish.
Persia was the leading world power at one time, in the ancient world of the Achaemanid (Hakhaimana) dynasty. Their civilization was the rival of the Greeks and Indians, although far larger and more powerful than the Greeks, and the envy of all Central Asian and Middle Eastern peoples. They conquered Egypt, Yemen, and Asia Minor as well as Afghanistan, the Caucasus, and parts of Central Asia. They were the first civilization to establish religious tolerance across their empire. Once taken into the fold of Islam, Persian civilization quickly became the major cultural influence across most of the Islamic world, including Central Asia, Turkey, the Caucasus, the Balkans, Tatarstan, India, and beyond. They see themselves as culturally enriching the Arabs and all other Muslim peoples, and the Arabs as having been uncultured desert dwellers before contact with Persia. In fact, the science of the grammar of the Arabic language was developed entirely by Persian linguists. Therefore, they do not accept taking a back seat to the Arabs when it comes to pride of place. On the other hand, the Arabs believe the Muslim world revolves around them, and the Persians and everyone else ought to take a back seat to the Arabs. That’s why there is serious, deep ethnic prejudice between the two peoples.
Persian is related to English (but not to Arabic). Compare: mother=mâdar, father=pedar, daughter=dokhtar, brother=brâdar. Persian belongs to the Indo-Iranian branch of Indo-European, while Arabic belongs to the Semitic branch of Afro-Asiatic. Indo-European and Afro-Asiatic are two unrelated language families. Except in the Nostratic hypothesis, which joins Indo-European, Afro-Asiatic, Altaic, and other families into one “macrofamily.” This would cancel the anti-Semitic bigotry of Nazism, since Aryan and Hebrew are related!!! But the time depth of Nostratic is at least 10,000 years BP, and the linguistic connections have been much obscured over the passage of time.
In any event, the relationship of Arabs and Persians is complex. Racially, they have been mixing genetically for over a millennium. al-Husayn ibn ‘Alî, the Prophet Muhammad’s grandson and a major figure in Shi‘ism, married the last princess of the Persian Sassanid empire. Poetry often refers to the two peoples (‘Arab and ‘Ajam) in tandem to mean the whole world, or at least the whole Islamic world. ‘Ajam means ‘non-Arab’, but in poetry refers to Iran.
New Persian (since the 9th century AD) has absorbed thousands of Arabic loanwords; Arabic is the main source of learned, legal, and technical vocabulary in Persian as are Latin, Greek, and French for English.
Arabic in its turn has taken on many Persian loanwords, including some of the basic terminology of the Islamic religion, like dîn ‘religion’. The formula of the Qur’ân “In the name of God, the Most Gracious, the Merciful” closely resembles a similar formula used in the ancient Zoroastrian faith, and the Islamic concept of the bridge sirât to the afterlife (which becomes wide and easy to cross for the righteous, narrow like a razor’s edge for the wicked) is exactly that of the Zoroastrian bridge chinvat.
The Persians and the Arabs have a long history together going back thousands of years; ancient Persia colonized several Arab lands in its empire, including Iraq (remember the Book of Esther?), Yemen, and Egypt. When Islam arose it rapidly extinguished the decrepit Sassanid empire of Persia and took the ascendant, but ultimately the whole Islamic world was vastly enriched by the fusion of Arab Islam and Persian civilization. I think this is the much more positive side of their complex relationship, and is ultimately more important than the petty ethnic and nationalistic rivalry between them in today’s headlines.