It's safer to do both (the CDs and the external drive).
The external drive is fine in most ways (but the fact you can over-write it means it is not immune from accidental (or deliberate) "let's delete these folders to make more room for these 400 GB of music from friend John" one day in the future when someone becomes a rebellious teenager and the "don't touch that" phrase no longer works.
Also, since the external hard drive can be written on, it is safer to unplug between backups. A virus wiping out files could spot the files on the external drive too.
These CDs are some of the more expensive the firm sells (they started off selling only blank CDs but now go on to sell blank DVDs, USB sticks, right up to PC systems.
So 14 quid (+ post) would get you storage for 60 to 70 GB (100 x 600 MB as you won't always find it easy to fill 700 MB with no 'unused' space) which should cover you for oodles of photos, and means that once written, a set can be kept at home, and after making another set, they could stay with parents.
It all depends how significant family photos are. As you already know, an external drive has many "pros" but some of the "cons" are that being so easy to write information on, things can equally be overwritten or deleted. The drive is relatively fragile - drop it from the desk and you have the {albeit low} potential to lose all data. Where years ago the smaller capacity drives often had 5 year warranty or "lifetime" warranty {for getting a replacement} the bulk of modern drives have only a year's warranty. Drives can be noisy, and it is therefore worth turning them off between backups. They are mechanical, so they can "die" just as easily as the main drive in your PC, which you copy "just in case".
Hope that's not too dreadfully depressing but for business, the rule is backup, backup, backup. Boring, but the sort of effort needed to feel safer.
Do a search for "grandfather, father, son backups" if you wish to go for a "belt and braces" strategy that has been in use for well over 30 years (something I learned about when I got my first job in IT in 1978).
Rather than spend 80 quid on storage of 1000 GB, you could buy a SATA drive docking unit and then swapping (for grandfather, father, son backups) just needs you to slide a different hard drive into the docking unit. You can buy one drive to start with, then add another 3 months later and so on. When you build up a library of music off iTunes (or from anywhere else), just buy an extra drive and stick a label "Music" on it, then add tracks to your external backup after buying new albums. It'll mean changing PCs in a couple of years is so much easier if you have peace of mind about having backup copies.