The difference is that bamboo is much harder and requires less resin than MDF and therefore has less energy dampening or suck-out caused by resin/glues.
Correct, it has a nice stiffness versus weight ratio. In my experience it can sound more "neutral" then other popular types of wood.
I did read one thing that I cannot seem to find a second time that claimed bamboo shelves bend over time, so they may be strong and stiff but sag under load. Not sure this is true as I could not find it a second time.
It can bend when loaded, if it does it's advisable to use a thicker board. I have not noticed it bending over time, but that's assuming using the "plywood type". There is a waterproof version for outdoors use which is similar to MDF, bamboo pulp mixed with resin, that can definitely sag.