What was a distinguishing difference between the military forces of ancient Rome and Carthage?

The Third Punic war was the only instance of Rome having the destruction of an enemy and the obliteration of a state as her war aim. Rome did destroy other cities in some of her wars. However, this was an outcome of military engagement and was not part of the initial war aim. Moreover, they did not involve the destruction of an enemy state. For example, the Romans destroyed Jerusalem after a long siege. However, this was not the initial intention and did not involve the destruction of the whole of Judea.

There was a similarity with Corinth. Rome destroyed Corinth, which was one of the cities of the Achaean League (an alliance of Greek city-states in southern Greece) which fought Rome. Both cities were destroyed in the same year (146 BC). Julius Caesar ordered the rebuilding of both cities as Roman colonies in 44 BC. However, again, destruction had not been the war aim in the case of Corinth.

The destruction of Carthage was advocated by a war party which won the day in Rome's politics. Their advocates argued that Carthage returned to prosperity and that there was a danger that she might rebuild her military might. This was not the case. Despite peace terms imposed by Rome after the Second Punic War which were meant to be economically crippling, Carthage did well. Her land was very fertile. It was one of the breadbaskets of the Mediterranean. Moreover, with the demilitarisation imposed by Rome she saved enormous amounts of money by not incurring military expenses. Later Carthage levied a military force to fend off attacks by her Numidian neighbours. However, she would not have been able to be a match for Rome's military prowess ever again. This policy was driven by resentment and fear due to the tens of thousands of Roman and Italian allies who lost their lives when Hannibal invaded. Carthage was destroyed and the 50,000 survivors of the siege were sold into slavery.