In allometric equations you don't need density (including wood density and bark density) to estimate biomass. but in volumetric equations you have to know the value of wood and bark density to estimate the amount of biomass.
Allometry is the most common and reliable method for biomass estimation.
Basically both of them are the same.
If you cant develop allometric equations by harvesting method (cutting trees) then you can use volumetric equations and wood density to develop allometric equation.