Great question! And there is a long answer to all this that is equally interesting as it is complicated. There are a bunch of answers to I encourage others to comment.

To understand the difference between the Republican Rome during the Punic wars and the western Roman Empire during the great migrations, we need to look at a couple of key things. One of these is the Antonine Plague.

It’s unclear what is was for 100% sure but it could have been some form of small pox. This spread via the extremely profitable trade route of India into Egypt, from the Red Sea. This plague was insanely destructive for Rome. It ended the Pax Romana ( debatable of course ) and through simple Roman traditions such as kissing when greeting someone, it spread like wildfire. It gutted the army, partly the reason why Marcus Aurelius was in the Danube in the first place, and it shattered basic government systems such as the tax system, which was never fixed ( remember that ) and it stopped silver mines, in which a large portion of Roman income depended on. The Cyprian plague would hit nearly a century later causing even more chaos and both of these plagues combined was a key reason but often overlooked reason for the crisis of the 3rd century.

So let’s fast forward to the fall of the western Roman Empire. Well the tax system was broken as I mentioned, so simple things like raising armies and maintaining them proved extremely challenging. This is why they relied so much on something like bribes, you don’t have to maintain a bribe ( most of the time ) and can just give it all at once, where maintaining an army is hard. This is also why they relied on mercenaries. These mercenaries were skilled, yes, but like Machiavelli said. Never use mercenaries.

Now let’s look at the Punic era Roman Republic. Well there tax system was fixed. So they could clearly have a decent army. They didn’t rely on mercenaries as much, and they didn’t need to bribe anyone. They had a large population and had not been hit by constant civil war or plagues. The Roman climate optimum which basically was a warming period in earths history meant that starvation was not going to be as common.

Also during the Barbarian invasions, it didn’t mean a whole lot to be a Roman, at least not as much as in the Punic wars. To be a Roman in 5th century Europe basically meant you paid taxes to the romans. The culture of “barbarians” and the romans had merged at this point in history and as one historian pointed out, it was romanized barbarians fighting barbaric romans. This combined with Christianity spreading and many Germanic tribes and barbarians converting only increased this process.

In the Punic wars, being Roman held more meaning than being a Roman in the barbarian invasions. In the Punic wars it meant from the city of Rome, or at least under its ownership. In 5th century it basically meant you lived in the empire.

So in summery, Roman identity, plague, broken systems never fixed, constant civil war, and the Roman climate optimum all played a role. I didn’t even mention the difference in military, the allies at hand, how Rome was so much larger and harder to defend, the corruption in the 5th century ect ect.

I will leave you with this though. I recommend you read “The Fate Of Rome” by Kyle Harper. He goes into some of those non mainstream details and if you like science, I think you’d like that.