The answer is long and complicated but I will start with the Europe. The Carp here are in their homeland, the closer to their[species] birth place the better they do, so carp in Hungary will do better than carp in Germany on average.
Up until recently the culture in Europe was to catch what you can and eat it, so carp never grew big at all, but now the iron curtain has gone and people have more cash, they would sooner buy a lump of salmon, so the carp do get chance to grow and because they grow fast it does not take long for monsters to appear, this combined with a relatively new movement of pleasure carp angling has resulted in the catches you hear about.
Next comes SA, the carp here are a mixed bunch bred from the original German fish and later aditions of Israeli fish and the can and do grow massive, somewhere in my files I have photos of 3 carp weighing in the 70-80lb bracket shot by two Irish lads at Umlilo. These came from a freshwater storage dam that was very deep with no shallows [very important]The carp were stocked by the bucket load and allowed to grow, no shallows so no breeding so plenty of food for the fish. However a lot of waters have perfect breeding for the fish and are then massively over populated.
Australia had its fish from, Europe and Asia, so two different sub-species of carp, where only European carp live the same rules as SA apply and they can and do grow big, however the hybrids etc. don't grow so big and on top of this the constant harassment by people works against the carp. New Zealand had its fish from Asia and these were what we tend to call Koi, they reverted to wild type, small long and lean.
But as already stated by others on this thread, the USA and Canada are a different ball game in that most of Canada does not have enough degree days to produce big carp, they get a great start because of warm water in summer but suffer in winter, so tend to grow quick for a few years and then slow right down, also they are mainly in rivers as the ponds, lakes etc are a predators playground, with Bass, Pike, Muskies, Trout, Sturgeon etc. and of course the otter. USA is the same in some senses with predators reigning supreme yet in other its the same as SA, they over populate and starve themselves out. One thing I will say is in quiet backwaters where carp can thrive there will be carp as big if not bigger than anything in Europe, but people have to fish to catch them.
I think I've covered it all there in a simplified manner, although I could add a lot more.