“Peaceful ancient Mediterranean state” is an oxymoron, the difference was a skill issue

What was the ruin of Sparta and Athens, but this, that mighty as they were in war, they spurned from them as aliens those whom they had conquered? Our founder Romulus, on the other hand, was so wise that he fought as enemies and then hailed as fellow-citizens several nations on the very same day. Strangers have reigned over us. That freedmen’s sons should be intrusted with public offices is not, as many wrongly think, a sudden innovation, but was a common practice in the old commonwealth.

…

Everything, Senators, which we now hold to be of the highest antiquity, was once new. Plebeian magistrates came after patrician; Latin magistrates after plebeian; magistrates of other Italian peoples after Latin. This practice too will establish itself, and what we are this day justifying by precedents, will be itself a precedent.

• The Roman Emperor Claudius

That being said, I must also note that, while Rome was not worse in the sense of being more essentially unjust or more imperialist than other powers, there is an element of brutality in Roman culture itself that was mildly exceptional.

The Romans, who never tired of praising themselves, admitted, regretfully, that human warmth was a virtue that their culture lacked. The Romans recognized themselves as a hard, callous people, and while some of this is chest-beating, there is an element of truth in it in that Romans both inured themselves to structured violence from a young age, and reconciled themselves to immense cruelty if done ‘procedurally’. The Romans also noted that the arena sometimes made ‘soft’ foreigners queasy - while this probably isn’t in reference to gladiators, but rather, public executions of noxii (criminals considered especially heinous, like traitors, bandits, murderers, and rapists), which could get quite… gruesome. Such as the famous ‘feed them to the lions’ trope.

On the other hand, there are any number of examples of horrific and arbitrary cruelty from other polities of the period. The difference is that the Romans generally (though not always) did so in a ‘cold’ and calculating way, while other cultures tended to do so after emotionally tumultuous events or by the order of capricious individuals.