Source: The Well-Educated Mind (2 edn 2016), pp. 254-255.
Aeschylus, Sophocles, and Euripides wrote tragedies; Aristophanes wrote comedies. Comedy, depending as it does on contemporary man- ners and morals to set up the jarring contrasts at its center, always dates more quickly than tragedy; a joke about politics loses its kick (try watch- ing a Jay Leno monologue from the Bill Clinton era), but the danger of wrong choices never goes away. The Romans, who came after the Greeks and stole most of their literary principles, wrote more comedies than tragedies—which is why neither the Roman playwrights nor Aristophanes are so widely read today as the Greek tragedians.
But even the tragedies of the Romans were inferior to those of the Greeks. Drama generally held a lower place in the Roman social scheme. Roman theater groups, like Greek troupes, acted at festivals. But while the Greek festival tended to be centered around play performance, Roman dramas had to compete with the more spectacular performances of lion fights, chariot races, and stadium sea battles. (In one of his prefaces, the tragedian Terence complains that the first two performances of his play were canceled because the audience left halfway through to go see the gladiator shows.) The Romans made no innovations in dramatic themes; these would come during the Middle Ages, when the Greek dramas had entirely slipped from view.
Wikipedia alleges the same scorn of Roman actors compared to Greek:
The public opinion of actors was very low, placing them within the same social status as criminals and prostitutes, and acting as a profession was considered illegitimate and repulsive. Many Roman actors were slaves, and it was not unusual for a performer to be beaten by his master as punishment for an unsatisfactory performance. These actions and opinions differ greatly from those demonstrated during the time of ancient Greek theatre, a time when actors were regarded as respected professionals, and were granted citizenship in Athens.[14][1]
What a fantastic question!! What you've asked requires that we look into the place that theatrical performances held within each society (i.e. Greek versus Roman). Now, it should be noted that theatre was never static in the ancient world and variations abound between locality and social function (i.e. Athens v. Syracuse--as both were Greek but they practiced theatre in different ways), but there are some comparisons we can draw that will help to provide an answer to your question.
First, let's look at ancient Athens since the examples you provide were from the Athenian Golden Age (i.e. the fifth century BCE) and constitute the foundations of the annual Dionysian festivals that marked the beginning of the trading season in March/April. The Athenian Greeks--and to some extension the Attic peninsula, Athenian colonies, and Athenian allies around in the Greek world--practiced theatre as a part of the festival known as the City Dionysia. For simplicity, I won't go into detail about the City Dionysia except to say that it marked a significant point in the Athenian calendar when citizens gathered to celebrate a patron deity and promote civic engagement among the various classes of Athenian society. As part of the City Dionysia, wealthy patrons (often politicians) sponsored the chori and production of plays that made up the main event of the festival. Essentially, the City Dionysia provided an opportunity where each Athenian demos (*δῆμος)--kind of like the suburbs and neighborhoods of modern urban centers--gathered together in a centralized manner such that the city-state was truly represented as a body-politic within the theatre itself. The actors and playwrights were prominent citizens and the themes they presented were meant to draw attention to particular socio-political issues important to their particular agendas and to the polity of Athenian society who had gathered at the theatre. That is why the Theatre of Dionysus, where the plays were performed, was prominently located on the side of the Acropolis and often served as a meeting place for Athenian political bodies. So, to keep this short, theatre was an opportunity for civic and political engagement that was foundational to the operations of the city of Athens.
This was not the case for the Romans. As you correctly identify, the Romans did not hold theatre to be anything more than a source of entertainment and distraction for the populace of Roman society. But it should be noted that Romans did hold similar (and largely borrowed) ideas about the literary nature of drama in regard to what it could teach a student of rhetorical and oratorical efficacy (see St. Augustine's explanation of his education in theatre in City of God). But perhaps the greatest indication of the role theatre played in Roman society was the lack of purpose-built theatre spaces. As you, again, correctly identify, much of Roman theatre was performed as a part of major festivals celebrating physical prowess (such as the Ludi Romani), marking the superiority of Roman people and Roman society. It wasn't until the 1st century CE that purpose-built theatres appeared in Rome itself! The plays of Terence and Plautus were performed on temporary stages erected in the Roman forum as an engaging form of entertainment--which rarely touched upon politically charged topics. The plays of Aristophanes, at least his earliest plays, were highly critical of socio-political goings on within Athenian society. I'm not an expert on all political things Roman, but the plays (i.e. comedies) of Menander, Terence, and Plautus were much more focused on domestic issues and were more broadly applicable to the Roman merchant classes, lacking the biting political commentary that made Aristophanes so successful in Athens a few centuries earlier. In essence, Rome was by no means attempting to replicate the democratic society of the Athenian Golden Age (however much it held it in esteem) and, as a more authoritarian state, was quick to quash dissent or critique or its political leaders or political acts. Therefore, acting was seen to be much more suspect as a profession. Though a play might have been written down, any performance was much more difficult to control. So, as a succinct conclusion, Roman society largely held drama to be an exercise in mere entertainment than in literary or performative meaning that could be utilized to [eventually] critique its leaders and social organization. So, the people who engaged in theatrical practices were not only suspect to the state, but were maligned in the documentary source that have survived from the early Roman periods (and, likewise, from Roman Christianity--but that's another topic).
Bibliography:
Performance and Culture in Athenian Democracy
Greek and Roman Actors: Aspects of the Ancient Profession
The Hypocritical Self: Actors, Acting, and Identity in Greek and Roman Culture