At first glance, this might seem obvious. So why is this so surprising?
First of all, not all courts in democratic countries are equal. A wide range of institutional variables influences judicial review by constitutional courts in Asian democracies. In Judicial Review in New Democracies, Tom Ginsburg finds a correlation between transitioning countries with dominant political parties and weak courts. Constitutional drafters can make courts more accountable to the government by shortening the justice's terms; restricting the court's jurisdiction; decreasing the size of the court; and making funding dependent upon other branches of government. As such, if a dominant political party drafts the constitution, it is more likely to design a weak court that it can later manipulate. On the other hand, a party that expects to to lose power at some point in the future would design a stronger court to protect it while out of power.
On the other hand, not all courts in authoritarian countries acquiesce to a marginalized role. In some regimes, courts play an important role buttressing the prevailing elites. For example the Iranian judiciary has at times actively supported the theocracy and undermined the legislative and executive branches when the latter were controlled by reformists. Some courts, such as Egypt's Supreme Constitutional Court, have even challenged authoritarian leaders and assisted liberal democrats. Constitutional law scholars have only recently turned their attention to courts in authoritarian regimes, although Tom Ginsburg and Tamir Moustafa's Rule by Law is a great start.
So, where does that leave Southeast Asia?
Constitutional courts in democratic Indonesia, the Philippines, and Thailand, as well as Burma during the 1950s, all exercise judicial review actively to strike down laws and executive acts. Philippa Venning argues that both the Indonesian and Philippine courts exercise "strong-form" review. Tom Ginsburg characterizes the Thai court as an important veto player. Reading about the Burmese Supreme Court, I've been struck at how justices played such an important role in Burmese politics, from striking down administrative acts to forming political parties. None of these courts would rank as the strongest possible according to constitutional design theory since they generally either have term or age limits for justices, but they nonetheless have tended to flaunt their power. None of the constitutional courts in the democratic countries have played a minor role or exercised judicial modesty.
All of the constitutional courts under authoritarian governments have submitted to government authority and none play a major political role. Courts in Communist Vietnam, Cambodia, and Laos have almost never challenged the dominant party-state. Likewise for the Supreme Courts in Indonesia and the Philippines during the Suharto and Marcos eras. As we saw recently, Burma's courts assisted the military in prosecuting political dissidents, including Aung San Suu Kyi. With a few exceptions, these courts have not issued shocking verdicts against the executive (I don't count the Philippine Supreme Court's decision to certify the 1986 election, since by that point Marcos was effectively on his way out). In fact, judges in these countries haven't received respect as elite figures or key political players (Sebastiaan Pompe tells some revealing anecdotes of the utter contempt with which Sukarno held judges). This isn't the result of "weak" civil law courts (as some scholars have argued). I suspect a combination of totalitarian party dominance in the mainland dictatorships and bribery in the insular patrimonial regimes has led to such weak courts when authoritarian governments reign. However, there simply haven't been enough comparative studies to make any firm conclusions.
I haven't mentioned Singapore or Malaysia yet because they stand midway between democratic and authoritarian - controlled by a dominant party, but also allowing at the exercise (if not substance) of democracy and civil liberties. Likewise, courts in both countries have a reputation of fairness when dealing with private rights and commercial cases, but have stifled political or public interest cases. Of course, Singapore's courts have a stellar reputation among the business community, but also vigorously enforce the country's libel laws. These courts seem to fall midway along the spectrum of judicial review, enforcing some private rights but refusing to interpret the constitution against political elites.
[As for Brunei, I honestly haven't followed Brunei's courts well enough to comment, but have heard nothing contradicting this post.]