The big one is why banks in rich countries are too big to fail. In Indonesia if there was a banking crisis, there is no way that a bank like BCA could be bailed out. There would be no alternative to failure and while there are concerns about overly predatory practices regarding consumer debt, it is different than it is in the US.
Instead the economy is built on a very different basis. 60-70% of Indonesians are self-employed. There are a number of corporations which have institutional investment (including some very large companies) but on the whole the vast majority of the actual economy runs on the basis of small business and the self-employed without investment capital beyond friends and family.
What this means is that the amount of control that banks have over the economy is lower. In the event of a banking crisis, people would find ways of continuing to trade and work, and you can't have the massive and debilitating layoffs that occur in the rich countries. In essence the banking system may be less protected, but at the same time, it is less influential and so while the effects of a collapse can be temporarily severe, it doesn't have the same reach that it does in the US.
A big part of the rich country trap is a economy that runs on investment capital, where the banks are a major source of that capital. A small-business-centric economy is far more robust against this sort of crisis.