I could ramble on this topic for hours... Pray that I do not.
It boils down to the severity of the secret nature of the data.
If you are concealing a crime or indiscretion or that second set of books the FBI has been looking for, then take the drive apart and fling each platter into separate bodies of seawater.
If your just not wanting someone to find your quicken backup or tax return then the hp destructive is enough.
Be aware that some systems cannot be restored fully to factory (OOB) status. Some vendors sell laptops and desktops that have restore disks that cannot recreate the original "restore" and diagnostics partition in the event of replacing a failed drive with a new blank one. You have to keep track of the recovery disks forever-after.
This is important if you run Dban on a disk with a built in restore partition and do not have full reinstall image disks from your vendor, it will securely and irretrievably blank the parts you want blanked as well as the parts you still might need.
HP always does a full restore since it sells mainly business systems and it is expected that they be regularly wiped and re-imaged with the company standard OS+apps image.
There are several tedious to arcane methods of backing up and restoring just the recovery partition and also how to transfer or recreate an mbr or a (u)efi partition but you will need to google around a bit to find those if you're interested.
If you really want to be destructive with the hp, you can run dban and just about any other program that calls itself a secure wipe and the hp recovery dvd is going to recreate the OOB (out of box) disk including recovery partition, efi if needed and the factory installed OS complete with bloatware, adware and (depending on the age of the system) you can get media programs that point to defunct web sites and cannot be uninstalled without hours of research, special software and a willingness to get deep in the registry.