If you have good pretreatment ...

If you have good pretreatment that will ensure removal of grit non-biodegradeable plastics and rags, it is often of advantage to eliminate the primary sedimentation as the anaerobic and anoxic stages need sufficient organic carbon for the slower digestion processes.  Some process designers like to still incorporate primary sedimentation and then digest the primary sludge to produce volatile fatty acids to feed into the anaerobic process for the phosphorous uptake bacteria to metabolise more efficiently.  However having a primary sedimentation stage does mean the primary sludge needs to be further treated as it is still very active as compared to an activated sludge.  So a more simple process excludes primary sedimentation with the advantage of simpler sludge management, but perhaps at the expense of less efficient phosphorous removal (unless the anaerobic stage and anoxic-anaerobic recycle is designed to improve this).  I hope others can contribute as I am not 100% certain of the precise dynamics.