They both have their ups and downs.
RAID 1 - Ups: All changes are saved to both HDD's with no need to set a schedule or run a program, HDD failure is solved by replacing the faulty HDD and the computer will automatically recreate the system mirror, no real loss of productivity while mirror is being created.
Downs - all changes are saved, if you accidentally delete a file, it will be deleted from both drives in the array. HDD's are internal and not portable.
External HDD - Ups: Can be used as offsite backup storage, if file gets accidentally deleted you can use the backup to restore it as of the last backup.
Downs: Need to run a program or schedule to run the backup or remember to do it manually, can be lost, stolen or damaged, upon HDD failure you would need to wait for the backup/image to restore new drive to usable levels.