This is a good question, but I think the premise is flawed. You seem to be equating size and population with power projection. If I were to reference a similar scenario such as the Roman republic against the Seleukid empire of Antiochos III, we can see why this is problematic. The latter empire was geographically larger and I would imagine held a higher population (sorry I don't know for sure, but it is an educated guess), yet the Romans were strong enough to assert their power over them.

The thought is Flawed. Persia, Mesopotamia and Central Asia, were for much of human history the most Urbanized and densely populated areas on Earth. By the Time Rome was founded Babylon was already older to them than Rome is to us. Their population was probably much more equivalent to Romes than you think.

By the time of The Sasanian Empire Rome was only half of what it used to be and embroiled frequently in other conflicts. As for Parthia, Parthia existed in a time when Rome had already stretched it's conquests as far they could go, many times the Romans were able to go deep into their territory and sack their cities, as was the case during Trajan's reign, but they did not have the ability to conquer them, so they each time would just regroup and re consolidate. They were simply an enemy they lacked the resources to utterly defeat.