Difference between the Pope now and the Pope in Tudor EnglandWatch
In all seriousness, I like the history of the Papacy, but I know not enough about it to answer your question.
I suppose you could simply say that the renaissance Popes had more authority, being a time where religiosity was taken very seriously.
The old Popes also had powers that could instate monarchs and excommunicate them (don't know if the current one still exercises excommunication) Take Alexander VI and his crowning of Charles VIII of France as King of Naples. Quite simply, the fact people were more religious then means that the pope was an incredibly powerful figure, arguably the most powerful in Europe. Of course, that authority began to wane throughout the reformation.
Most of them would have been Italian also, I believe pope John Paul II was the first non-Italian in hundreds of years.