ESCRT proteins participate in the fission step of exocytic membrane budding, by assisting in the closure and scission of the membrane neck that connects the nascent bud to the plasma membrane. However, the precise mechanism by which the proteins achieve this so-called reverse-topology membrane scission remains to be elucidated. One mechanism is described by the dome model, which postulates that ESCRT-III proteins assemble in the shape of a hemispherical dome at the location of the neck, and guide the closure of this neck via membrane-protein adhesion. A different mechanism is described by the flattening cone model, in which the ESCRT-III complex first assembles at the neck in the shape of a cone, which then flattens leading to neck closure. Here, we use the theoretical framework of curvature elasticity and membrane-protein adhesion to quantitatively describe and compare both mechanisms. This comparison shows that the minimal adhesive strength of the membrane-protein interactions required for scission is much lower for cones than for domes, and that the geometric constraints on the shape of the assembly required to induce scission are more stringent for domes than for cones. Finally, we compute for the first time the adhesion-induced constriction forces exerted by the ESCRT assemblies onto the membrane necks. These forces are higher for cones and of the order of 100 pN.