No currency can perform perfectly for everyone living in the currency zone. Some areas will need easier access to money, while others would benefit from tighter monetary policy. Complementary currencies can help different parts of an economy receive the monetary policy that best suits them, even when the overall economy is going in another direction.
One of the well-documented problems with the Euro currency (there are also many good things, this is not about bashing the Euro) is that different countries may need different monetary policies at different times. When a country is in recession, it needs easier access to money, and a country with a booming economy may need to tighten the money supply in order to avoid inflation. The European Central Bank (ECB) has to balance these needs when creating policy and thus many countries end up with a monetary policy that is not ideal for them.
The same problem exists for geographic areas or economic sectors of any large economy. There will always be sections that need different policies.
Complementary currencies can help ease this problem. When a company could benefit from monetary easing then it can do that for itself and not suffer with a bad policy from central planners. The same is true when a company could benefit from a tighter policy, it can just decrease the amount of its own complementary currency that it is using. The companies that do this well will receive great benefit from it, as will their workers and all other stakeholders.
These benefits from the individual components of an economy can add up and result in an overall economy that is functioning at a higher level. Thus, a monetary system that uses complementary currencies can produce better policy that leads to more stability and greater growth.