Carthage relied on mercinaries, Rome didn't. Rome had huge reserves of manpower-if they lost a fleet of 100,000 men they just built another one and were thankful the crowds in the forum had thinned out a little.
Rome's "allies" weren't as solid as some would make out, when Hannibal invaded Italy many of them sided with him including Capua. The Bruttians were so anti Roman they formed the backbone of Hannibal's last stand at Zama.
Rome extended the rights of citizenship to the areas it conquered, allowing people the chance to be part of the ruling elite, or at least be afforded the same rights as the former "enemy"-a big reason for their success