The prime differences will include the removal of the wiring looms serving the permissible action links (PAL.) The PAL enable the manual entry of a specific code or series of codes, without which the weapon(s) may neither be armed nor released
Also some aircraft, (viz the Canberra B(i).8) have or had particular weapon pylons that are specific to one or more types of nuclear weapon. These pylons, are not compatible with conventional weapons. (In order to eliminate the possibility of loading a nuke in error.)
On a more human level crews of conventionally armed aircraft are unlikely to be trained on the very specific procedures associated with the carriage and delivery of of nuclear weapons.