The often citied rule is that the Roman Maniple was more flexible and therefor defeated the more static Phalanx. While technically true, in that the maniple was able to operate more effectively over rough and uneven terrain, I don't think there is enough evidence to show that this increase in flexibility was the deciding factor in Rome's engagements with the East.

The Battle of Cynoscephalae was lost more due to Phillips tactics creating disorder in his ranks. The Battle of Magnesia, was won by a flanking calvary maneuver in the same spirit as the Macedonian Hammer and Anvil. The later Battle of Pydna Rome had to make use of a tactical retreat over rough terrain after losing the initial engagement and showcases more the discipline and experience of the legions taking advantage of a weakness, than an inherent superiority in organization and composition. These three battles can all be looked at in comparison to the earlier battles against Pyrrhus of Epirus who won twice against Rome, and as legend has it had the Romans on the verge of themselves suing for peace.

There is really nothing to show that the Romans army composition was comprehensively superior to the Macedonian Phalanx. What is clear is that Rome did learn from Hannibal the importance of positioning and terrain. That it was critically important to have an enemy army fight on footing that is unfavorable to them. It also show the strength of the political confederation that they assembled in Rome. Roman Italy could take a punch, Rome could lose a battle, raise more legions and carry on the fight. In contrast the Macedonian states were far more fragile. Any decisive battle in the field had them suing for peace and took decades of recovery. Its my opinion that the superiority of the Roman ability to coordinate the resources from their Italian Socii that was the real power of Rome.

I am linking Wikipedia here for convenience. There is also a great book called Rome Enters the Greek East: From Anarchy to Hierarchy in the Hellenistic Mediterranean that covers this in time period in detail from a International Relations standpoint.

Swinging back to answer your Question the Sarissa Phalanx fell out of favor as each of the Successor Kingdoms was diminished and dismantled by the expansion of Roman power in the east. Once the political and cultural institutions that had supported the Sarissa Phalanx had failed that model of army fell out of use. Toward the end of the Hellenistic era, Pontus under Mithridates tried to replicate the Roman style though with little success.

Up until their conquest by Rome essentially. The superior maneuverability of the Roman manipul system enabled them to defeat the phalanx based armies of the Hellenistic kingdoms one after another in the years between the second Punic War and the Roman civil wars.

Thanks everyone for their replies, special mention to u/LeftoverNoodles and u/sk5952 - I've learned a lot!