I mentioned South American paleontologists defending the honor of their extinct animals, and pointed out how stupid that is. There are many similar cases: Jefferson vs Buffon on the wimpiness of North American mammals (as a reader pointed out), biologists defending the prowess of marsupials in Australia (a losing proposition) , etc.
So, we need to establish the relative competitive abilities of different faunas and settle this, once and for all.
Basically, the smaller and more isolated, the less competitive. Pretty much true for both plants and animals.
Islands do poorly. Not just dodos: Hawaiian species, for example, are generally losers: everything from outside is a threat.
Next up from islands is Australia: still losers. The only invasive species I can think of that originated in Australia is the brushtail possum – and it invaded New Zealand. That’s like a dwarf beating up a midget. Birds can be an exception – they aren’t really isolated, if they have good powers of flight. Some say that crows originated in Australia. By the way, there is a chance that penguins originated in New Zealand. I suspect that NZ’s faunal backwardness might have aided penguin evolution, for reasons that I leave as an exercise for my readers.
South America: not as embarrassing as Australia, where the local predators are out-competed by house cats, but South America’s only competitive mammal export is the nutria, as far as I know. The locals did poorly in the big interchange with North America, after the formation of Panama.
North America has had lots of contact with Eurasia, is fairly big, hasn’t really been isolated. Important lineages like horses and camels originated in North America. That said, some elements of the North American biome seem uncompetitive – seems like freshwater fish are pretty vulnerable to invaders. And Eurasian steppe imports do pretty well – things like tumbleweed and cheatgrass.
Africa was an island continent for a long time: although some of the Afrotheria have done well, particularly elephants, most have not. As far as I know, there was only the one mammalian lineage in old Africa, which may have limited local competition.
Eurasia: if you can make it there, you can make it anywhere. the two biggest placental clades, Euarchontoglires and Lauriasiatheria apparently originated in Lauriasia (Eurasia plus North America) . Between them, they account for more than 95% of placental mammal species.