Unstable nations are unpredictable and often very radical in their actions. A perfect example of this is Sudan and the Darfur area. Where a Muslim government, is essentially eradicating the indigenous tribal population in what is essentially a hate-field genocide. If this region was stable and developed, the population would be more educated and also less prone to blind hatred and animosity.
Unlike an unstable nation, a stable nation has more financial resources, more power, typically a better-organized military, and better leadership. Although failed nations can be unpredictable, as you stated, they normally lack the leadership and resources to pull of anything threatening.
There are uneducated people and leaders in developed nations too. Example- The US under George Bush
I disagree with your statement that underdeveloped nations can not hurt us as greatly as developed, because many underdeveloped nations have the ability to produce weapons with the potential to cause the irrevocable and crippling harm to the United States. For example, Iran, which is currently in peace talks with the U.N., was discovered to have a nuclear power facility hidden in the mountains. This facility was found to posses the technology necessary to convert unrefined uranium into the refined uranium used in nuclear bombs. While this motive has not been fully proven, because this information is known only by officials from the corrupt Iranian Government, the unveiled of this base by the United States Intelligent certainly shows that even the most underdeveloped nations can produce the most extreme weapons used in warfare. It can be assumed that the turmoil and dictatorial nature of these governments makes them a greater threat than developed nations with the same weaponry.