Main difference is that animals were hunted in the past primarily as food animals and populations were kept low enough that this limited growth. If you wanted meat you killed something in the woods if you found it. You killed enough to lay up for the entire winter. In the Old World the same, wild cattle basically eradicated, other large animals reduced as populations grew.
Now every goes to the grocery store and lives on pigs from farms or beef and chicken. There is little food hunting, which doesn't mean they aren't being eaten, it means they are not being hunted primarily for food, they are being hunted for sport, lots of hunters don't eat what they shoot.
Also, few large predators other then men now.
And now, there are crops everywhere, so lots of food sources.
So the swine population explodes and with more pigs, it grows even faster. When there are a dozen pigs, the young can get killed fast enough to keep populatons down, with hundreds, you can't kill them fast enough anymore.
