There are more reasons why they have lots of kids in the third world. Obviously they prefer males over females. That's because males can work harder and be more economically effective, of course, but religion and other social issues that don't play a big role in the west also have a part in that. So if you need 3 boys you'll most likely need to have at least 4-5 kids in total for that. Secondly, because of diseases and stuff many kids die even before they are able to work, so they'll have to have a 'backup' kid (as horrible as it sounds). And that's a magic circle, because someone who is born to a poor family with many kids has no chance to succeed at all. He'll, too, be poor and have many children, and so it continues...
In the west there is no problem of overpopulation at all (in fact I believe that in some European countries the population growth is negative, discounting immigrants) - it's mostly about over consumption.