Solid rivets present a larger challenge when de-riveting.  The manufactured head must be ground or milled off prior to pushing the rivet back through the hole.  When removing solid rivets, the material of the component surrounding the hole must be considered.  If the material is softer than the rivet, there is a chance it will be damaged.  If the hardness is equal to or harder than the rivet the risk of damage is lower, as it will maintain its shape while the softer rivet is pushed back through.  How the rivet was initially formed also plays a role in the de-riveting process.  The larger the shank swell created in the forming process, the higher the risk of damage to the surrounding component.