Given that sustainable development integrates needs of the people, and takes into account limitations in technology and social organizations, public awareness and economic development are important. The levels of importance may be contextual and site specific.
I think that awareness is more important as sustainable development includes to use resources wisely which might be contra-productive for economic development, at least to economic development, which is measured through economic growth. Economic growth reflects on waste of resources, environmental degradation and similar positive, contribution to growth of GDP.
They go hand in hand because economic development is driven by public demand. The public writes the software programming for economic development. Education (informed consent) is a key driver of public demand. However, at some catastrophic point of ecological collapse, when we can no longer afford the luxury of education, economic development will be driven by the need to survive.
Only a small restricted aspect of Economic Development is actually part of Sustainable Development. It is essentially impossible to start with any of the various definitions of Economic Development and pare it down by applying the restriction of 'needs' and 'ecological services' without the resulting definition being either unworkable or too fuzzy to be useful.
Public awareness would be a good idea, except that the concept of Sustainability has been hijacked by marketing efforts - one would have to start by setting out a set of detailed and self-consistent definitions that can be supported by all of the various stakeholders. VERY difficult.
So, once you have a good set of definitions, you'll be able to answer the question.