In oracle XE, what is the difference between the autobackup and backupset direcories?
AUTOBACKUP, by default, contains automatic backups of the controlfile and the spfile (if the database has one), if the AUTOBACKUP feature is enabled.

rman target /
show all;


There you should see:

CONFIGURE CONTROLFILE AUTOBACKUP OFF# default


Or ON, if it is configured. With AUTOBACKUP enabled, the controlfile will be automatically backed up on backup operations, and on changing the structure of the database (e.g creating a new tablespace, adding a new datafile). In 10g it is performed immediately after changing the structure, starting with 11.2, it is performed a bit later (Controlfile Autobackup Deferral), allowing the execution of multiple structure changes without creating an unnecessary controlfile autobackup for each action.

BACKUPSET, well, that is where all other backups go, by default. Backups of the datafiles, archivelogs and controlfile and spfile backups if AUTOBACKUP is disabled, or created explicitly.