The rigid floor diaphragm assumes infinite in-plane stiffness of floors and therefore reduces the size of stiffness matrix as a result analysis is generally performed faster. The semi-rigid diaphragm uses the actual in-plane stiffness of the slab elements and does not condense the stiffness matrix. For most concrete structures where slab is sufficiently thick and you expect negligible in-plane deformation due to lateral loads , results for semi-rigid diaphragm will be very similar to those for rigid diaphragm. However, if you are expecting significant slab in-plane deformations or when required by code, then modeling a semi-rigid diaphragm will be the correct way to handle such cases. A semi-rigid diaphragm is the same as assigning no diaphragm except that it allows you to assign accidental eccentricity due to Seismic load cases. Additionally if in plane forces on a slab or beams(i.e.chord, shear, collector diaphragm forces) need to be retrieved a semi-rigid diaphragm must be used.
See also: https://wiki.csiberkeley.com/display/etabs/Accidental+eccentricity+in+ETABS
