The rise of the Sassanian dynasty in the first half of the third century is often mentioned as an event that had a major impact on the history of the Roman Empire. Reason being that the Sassanid Empire was a more powerful state than the previous Parthian Empire and so Rome had to rethink its defense strategy in the eastern frontier.
Indeed, the Sassanid under Shapur I had many successes against the Romans, going as deep into roman territory as Antioch. Those campaigns are the evidence that is used to defend Sassanid superior military power compared to Parthia. They had more success against Rome therefore they were better at waging war.
However, as Adrian Goldsworthy notes, the Sassanid and Parthians were essentially the same people, only ruled by a different house. And so it's expected that their armies wouldn't be that different in aftermath of the fall of the Parthians as the rulling house.
So my question is, do we know how the early Sassanid army looked like (say before IV century)? How similar or different it was to the earlier Parthian army? What tatics it use and stuff like that?
Gratitude.
I believe it has a great deal to do with the consolidation and centralization of power that Ardashir I and Shapur I worked to achieve. The Parthian ability to mobilize forces depended on hundreds of petty lords.
What's more, it's worth noting that the Parthian empire did have plenty of successes against Rome. Ardawan held his own against Caracalla near Nisibis. The 218CE treaty was very much in the favor of the Parthians, which speaks for the capable late-Parthian military.
So I don't think it's as clear cut as you're imagining it in terms of military strength. Rather, support and administration. I admit that while I'm very familiar with the Sassanian military, my familiarity with that of the Parthian military is wanting. Just going by history, and some military conventions and units that have endured in Iran (such as cataphracts and horse archers).