[inglor_cz]

"Rome was the rising and expanding power. Carthage was an old has-been. "

This sounds like "reading history with a benefit of hindsight". Rising powers may, in fact, well lose their challenge against the old has-beens. Germany and Japan in the 20th century were those rising and expanding powers, but ultimately reaped catastrophic defeats.

Rome survived and won mostly due to their enormous capability to reconstitute their forces after major losses. That was an untypical capability in the premodern world, where a single battle gone wrong (e.g. Gaugamela) could topple an entire empire.

But major losses they did have and the fact that they could still hold after Cannae was a bit of a miracle. They even recruited slaves into the army, a feat that could have easily backfired against the weakened Roman elite.