In theory, yes. High stiffness woods tend to be able to store more energy per unit of mass. But mass can be distributed such that the mass of the bending portions hardly affects tip and lower limb mass. And then other wood properties come into play too.
So PatB said it already.
Low stiffness woods for their mass are ERC, osage, yew, elm, plum
Medium stiffness woods are ash (some), hickory, maple, black locust, ...
High stiffness woods are birch, eur ash, bulletwood, douglas fir, bamboo ...
All can make very good bows. Low stiffness woods are preferred because they can stand abuse better, including changes in ambient moisture. Moisture management is less critical there.
Bamboo is popular as a backing because it has high stiffness and being able to tolerate high strain for its stiffness.
But it could be that high stiffness woods also suffer more from hysteresis.