localtimestamp or curent_timestamp for default value

In Oracle-12c I have some columns that I am converting from timestamp with time zone to timestamp with local time zone. Some of those same columns also currently have a default value of CURRENT_TIMESTAMP. Should I change the default values to use the LOCALTIMESTAMP function instead? The columns seem to populate fine if I just leave the CURRENT_TIMESTAMP default values. Is there any practical reasons or gotchas for using one over the other in this case. I have been combing the docs but can't find anything.