Rome was found later than Carthage and was built on farmers and soldiers.
Carthage came before Rome and was built on wealth and traders.
The first Punic war started when the Carthaginians attempted to take over Sicily. That lead to the Romans and Carthaginians fighting over the island.
In the second Punic war, the Carthaginian general, Hannibal, traveled across the Alps to get to Rome.
After the second war and Carthage had paid off a huge indemnity and Rome didn’t have any interest in keeping them alive, Rome had asked the Carthaginians to resettle. They took offense to this and that started the third Punic War.
After the three Punic Wars, Rome had become greater than Carthage and left the Carthaginians poor.