Will it be more efficient if airplanes flap like birds?
In short, the answer is No. For many centuries, many proto-aeronautical engineers believed that the secret to manned flight would be found in complex flying machines that mimicked the flapping techniques of birds. These ornithopter designs were doomed from the start.

Aside from the obvious issues involving strong, rigid, durable, and light materials, there are tremendously complex psycho-muscular factors involved in biological flight mechanics that are impossible to duplicate with machinery. A bird has the benefit of nerve endings all over its body which provide immediate and intimate feedback of every minute shift and change. Additionally, the bird has fine motor control over its flight surfaces to a much greater degree than any aircraft can realistically replicate, and all at the speed of thought.
The good news is, efficiency can be relative. While the deft flight of a bird can be graceful, beautiful, and evolutionarily effective for its avian lifestyle, it will certainly never accomplish a trans-Pacific trip at 500 knots. Mankind has learned a lot from watching our feathered neighbors, but ultimately, our journey among the clouds lies along a different path from theirs.
That said, some small drone applications show promising possibilities for mimicking insect wings, so mother nature may still have a few more tricks to teach us.