- But you don't have the same transmission as the wheels are part of the transmission. Smaller wheels are not as efficient - more rolling resistance. You also need to send more chain which is not as efficient.
- You don't have the same position and lack multiple positions offered by drop bars.
- The frame is not as rigid and absorbs pedal energy.
In the end if you don't notice a difference and like riding the bike then that is all that matters.
Some comments on rigid.
A compact frame is not going to be as stiff as full size frame.
A hinge is not going to be as stiff as a solid tube or welded joint.
Birdy does some cool stuff to retain side to side rigidity in the way it folds on its own plane but it is still a small hinged frame.
You said touring. The second picture is a touring bike that is about the same price.
I am not associated with Salsa other than I own one.
That single single top bar is going to have more side to side flex and and twist than a large triangle. With the taller handle bar stem and seat post there are also a longer levers to exert flex. That flex is not recovered as pedal energy - at the bottom of the stroke the flex comes out and it does not go back into the chain. The rear triangle is clearly going to be more rigid than a single hinge.
Birdy is cool bike. I am not putting it down. You asked if a folder was as efficient. A strong rider on a Birdy could hold with me on my Vaya but I am in my 50s.