I believe that, when comparing the efficiencies of representative democracy and direct democracy, direct democracy is far less efficient. Since efficiency is relative, I believe this answers the question.
I'm taking "efficient" to mean "able to pass laws, policy, budgets, etc. In a reasonable amount of time that are reflective of the majority's beliefs". With that as our goal, I don't think direct democracy is any more efficient because it requires the entire population to be informed and involved in the process of laws. I really can't think that retrieving the votes of millions of people and counting them, AFTER granting enough time for them to become informed on an issue, make suggestions and revisions, etc. Could possibly be a practical way to solve the vast number of problems facing the modern country.
Furthermore, even career politicians can't keep up with the thousands of decisions that government has to make and place much of the decisions on advisors/experts. To expect citizens with jobs to be informed enough to make intelligent decisions on every issue is impossible.
Summary: direct democracy is unpractical and an impossibility for the modern country, let alone efficient.
By contrast, representative democracy, though it may seem inefficient at times, is a system that is far more practical and efficient (though perhaps the implementation in America could use some work xD)
Democracy is effective either way, whether implemented or attained over time. It allows people to adjust to the idea, or form their own unique way of doing things which is exactly how a place trying to obtain democracy should be, creating their own ways and laws that fit with their people.