There's considerable variation in the education methods in the [East] Asian countries. Also I've found a tendency amongst some to play up the rigour of education systems in the East Asian countries. It's really not that extreme - a lot of us (Singaporeans) grew up playing a lot of computer games, going to compulsory sports/student club activities, religious activities, etc. Whereas the Chinese system is harsher on the kids in terms of raw work required and rote memorisation needed.

So on average, East Asian countries have tougher/less discussion-based schooling cultures/systems compared to non-East Asian countries. But there is significant variation within East Asian countries. Note also that Singapore is strictly Southeast Asian, but racially it has a Chinese majority. Asia is really big. When Americans say Asian they mean East Asian (Chinese, Korean, Japanese, Mongolian, etc.). There are also South Asians (India, Bangladesh, Pakistan, etc.), Central Asians (Kazakhstan, Russia east of the Urals, Azerbaijan, etc.) and Middle Easterns (Arabs, Israelis, etc.).

If you ask me what is lacking in stereotypically East Asian education systems, it is not academic quality. Our education and culture tends to produce people who are risk-averse, followers as opposed to leaders, un-aggressive, non-confrontational, passive-aggressive - just look around the USA to see how many [East] Asian accountants/lawyers/engineers there are, and how few leaders/CEOs/entrepreneurs (even if you account for discrimination against visible minorities in high corporate positions). That's a much bigger problem than "our kids don't dominate the International Mathematical Olympiads". Intellectual achievement up to a point is useless further on, without being backed up with good old-fashioned aggression and ambition.

Source: all my education pre-University was in Singapore, University education in England.