The Parthians entered the scene near the hight of Roman Power. The Huns towards the final collapse of the Western Empire. Parthia had a very limited frontier with with the Eastern Provinces, the Huns operated over the huge Rhine / Danube frontier. There is also what is probably a historical prejudice that the Parthians were unable to take walled cities and forts, but the Huns, like the much later Mongols, were fairly adept at siegework

What I would attribute as the most important differences, is that it currently thought that the great migration of Germanic Tribes into the western empire happened because of Hunnic attacks into their hinterland, and it was the combination of these marauding Germans and Hunnic Armies that throughly overwhelmed the Romans, and the Huns encountered the Romans after the Crisis of the 3rd century against a Rome that was relative to her neighbors far less powerful.

I agree with the other comments but would say that it's an over-generalization to claim that the Parthians were dominant vs the Romans. The border between the two empires was, after all, in Mesopotamia not along the Adriatic, and Ctesiphon was sacked by the Romans multiple times.

I think an additional factor was that the Huns were nomads, and the Parthians lived in cities and so had fixed, valuable property which could be attacked, sacked, and ground held. If your army runs away and isn't defeated, but the enemy burns your capital, is that a win? While the nomads simply withdrew when faced with strong resistance, and had nothing to destroy or possess.

The Romans defeated the Partains in many decisive battles and sacked thier capital at least once. I think that it comes down to generalship, and when the Huns came the empire could not field any army with capable leadership the majority of the time. The armies themsleves were very different in the later years with the West relying heavily on the 'foederati' who were barbarain peoples settled in Roman land who were fighting on behalf of the Empire. These armies had questionable loyalty and different compostions than the tradiational army of High Empire that was fighting the Partians.

Would like to elaborate more but hockey is on!

Additional question: The Romans started adopting mounted archers after their encounters with the Parthians and mounted archers were a big component in the Late Eastern Roman Empire's (Byzatine) military but how quickly and widely were mounted archery adopted and utilized?