Why did Catholic missionaries have their greatest success in Spanish America and in the Philippines?
There are two main reasons for this.
First, these two areas were much less developed economically and socially than other places like Japan and China. The Spanish quickly came to dominate the economies of these places in a way that they did not do anywhere else. This made it more likely that natives would convert as a way of getting ahead economically and socially.
Second, the Spanish had much more control over the natives of these areas. The natives were often essentially serfs who were bound to Spanish masters. This gave the Spanish much more of an opportunity to influence their religious choices than was true in other places that Catholic missionaries tried to go.