As the ESRI WEBHELP clearly describes: " Checking this option causes edits that have been saved to the DEFAULT version, whether edited directly or merged from other versions, to be saved in the base (business) tables. Edits to other versions remain in the delta tables when you save.
This option is available for simple features only�??those that do not participate in a topology, network dataset, or geometric network. Therefore, if you open the Register As Versioned dialog box and find the move edits to base tables check box is unavailable, it means your dataset contains a topology, network dataset, or geometric network.
Registering the data as versioned without the option to move edits to the base table is beneficial because the other option does not allow for conflict detection, nor replication.