I don't think Hannibal ever intended to completely destroy Rome, just defeat them and make them suffer. Plus, the Romans are tenatious, you would have to kill off nearly all of them to completely stop them from comming back.
But as for the question, the whole world would have been completely different. Modern western society is based off of Roman and Christian origins.
I doubt Carthage would have taken Rome's place in history, but without Rome the Parthians and Sassanids would have been more powerful and may have tried invading Europe at some point. Also, the Gauls would have someday become united and powerful.
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