Well, before this question is even answered, I think your premise needs to be seriously questioned and elaborated on. Did the Islamic Empire become 'persianized'? What do you mean by this specifically and to what extent? And which Islamic Empire are you referring to? The only caliphate that can singularly be referred to as 'the' empire is the Rashidun Caliphate. But as is very topical knowledge on the matter, Persian influence didn't really become pervasive in the Islamic context until well into the Abbasid era.

Despite there being significant Persian influence on the Caliphate(s) in their early/middling phases, '-ization' has a very specific connotation in conventional use, and I think your premise that 'the Islamic empire' was Persianized is at the very least debatable.

A better way to frame this question might be "why did Persian society have a greater influence than the Byzantine on the medieval Islamic world?". And even then, that is in my view a debatable premise. I know it's just semantics, but semantics is a critical aspect of historiography.

Not all Islamic Empires Persianised. Which one are you thinking of?