Christianity growing faster than Islam?

I know that more people convert to Christianity every year than to Islam, but I thought Islam was growing faster because of a high birthrate among Muslims, especially in countries in the Middle East and places like Afghanistan and Pakistan, where birth rates are very high. But Diniesh D'souza says no, check it out and see if you agree with him:

Is Islam the Fastest-Growing Religion? Guess Again
by Dinesh D'Souza

Many people think Islam is the fastest-growing religion in the world. Not true. Islam is growing fast, but Christianity is growing faster. Indeed there are twice as many Christians as Muslims in the world today and the gap is becoming larger. Moreover, Christianity has become the world's only religion that is truly universal.

Islam too has a wide reach, but Islam has only a small presence in the United States, Canada, Central and South America, and Australia. Christianity, by contrast, is strong everywhere in the world except the Middle East. Islam is growing mainly through reproduction, which is to say by Muslims having large families. Christianity is growing both through reproduction and through conversion.

So if Christianity is growing so fast, why don't we see it? Because the growth is occuring mainly in Asia and Africa. The full story is told in What's So Great About Christianity but here are some examples. In 1900 less than 10 percent of Africa was Christian. Now it's around 50 percent. That's an increase from 10 million Christians in 1900 to more than 350 million today. The story is pretty much the same in Asia. China now has an underground church numbering in the tens of millions. In Korea, Christians outnumber Buddhists and, in a remarkable historical reversal, now send missionaries to Europe to convert the natives. Some Asian and African churches have so many members that pastors have to tell people not to come very Sunday, because there is not enough room in the pews. [...]