It is a little bit difficult to know how to answer this question as much of what we know about the Persians comes to us from the Greeks. This means that we may not have a truly fair view of what the Persians were like and what the world would have been like had they defeated the Greeks. However, historians often say that the modern world would have been much different had the Persians won the war.
Historians say this because the civilization of the Greeks has been the basis for much of our modern Western civilization. This is particularly true of our public life since it was the Athenians who were the first that we know of to have a democratic society. They passed their institutions on to the Romans and, through them, to us. If the Greeks had lost, it is possible that there would not be any democratic countries in the world today.
The Greeks also contributed greatly to our culture. They gave us things like tragic and comic theater. They gave us the writing of history. It can be argued that we would not have these things if they had lost.
Of course, there is no way to know for sure. For example, even if the Persians had won, there might still have been a chance for democracy to develop. However, it is typically said that the Greek victory in this war made our modern Western world possible.