In what sense did the Columbian exchange not have "such an effect" on Asian cuisines? I don't mean to disparage your question -- but you may simply be unaware of the great impact of New World crops in Asia.

Just a few major crops that became staples in some or all parts of Asia include potatoes, sweet potatoes, tomatoes, peanuts, corn, guava, cashews, cassava, capsicum (chili and bell peppers), pumpkins, kidney beans, many types of green beans, and numerous others. There can be no doubt that pre-Columbian cuisine in almost every corner of Asia would have looked very different from what one would have encountered at the turn of the 19th century. This cannot be emphasized enough.

Given how transformative the Columbian exchange was to Asian cuisine, I have to ask -- what specifically leads you to ask this question? I might remind you that what you "hear about" hardly represents the reality -- one hears more about Western history in general. One might also just lack knowledge of Asian cuisines. For example, an American might be surprised to learn that the kidney bean is a staple food in North India simply because Indian-American restaurants tend to exclude it.

That isn't to say that there is no substance at all to your question -- there are certainly some crops that had a greater impact in Europe (and others that had a greater an impact in Asia). A variety of factors would have an effect on this, including the climate, government intervention (for example, encouraging or even enforcing the cultivation of potatoes), religious dietary restrictions, and, of course, culinary concerns (i.e. taste). In addition, some crops just took longer to reach Asia, whereas others did not. In order to get an answer, however, you would have to qualify your question.