Sufficiently long term, everyone is dead, and I am not sure if we can tell those long-term effects that you foretell from random chance.
The Roman Empire is very dead, but so is the Carthaginian one. Nevertheless, a lot survives from the Roman Empire: basics of law, their alphabet, descendant languages and a certain fame. Quite a lot for famously war-like people.
In comparison, the Carthaginians are gone completely, only fans of history know anything about them. And they are gone because they lost a series of wars all too decisively.