These days, HDD; with SSD coming a strong second, or even first but for price - though that could change in a few years.
I can only really back this up anecdotally, though Backblaze have some large data sets of which HDDs are surviving best. They provide a report & links to the data every quarter. Most recent is One Billion Drive Hours and Counting: Q1 2016 Hard Drive Stats
One additional factor to bear in mind is that the Backblaze stats are for drives which are constantly in service, not simply stored in a cool room.
Every music project I ever made is on an HDD in a box, some going back to the 90s. Haven't lost one yet. The transition from SCSI, through PATA to SATA meant copying to newer & usually larger drives periodically - which is always going to be an issue as standards change.
Two copies of every drive is sensible. A third off-site is belt & braces.
I do the same for movies, though in a less-fastidious fashion - I don't actually take the drives out of my media machine until I can get no more in, nor do I back up movies drives. Currently I've about 16 TB of movies.
As that system gets older, I would probably transition to NAS next.
HDDs have had the best price per MB for quite some time now, with 4TB coming in at around 100 quid/bucks/shekels.
Cataloguing is done through a file database/catalogue app - NeoFinder in my case - though there are many out there to choose from.
I have some projects going back to the 80s that I had to transfer from reel-to-reel. I only had facilities to transfer the ¼" tapes, so I lost a lot of material that was on ½" & 2" - not a scenario I would ever like to repeat.
I nearly lost the ¼" too - the tapes were early-mid 80's Ampex 456; which turned out to have a disastrous shelf-life.
After months of research, I eventually built my own tape-baking rig, which was very successful - I did azimuth & EQ correction afterwards, so each tape only needed a single pass & I successfully saved the entire collection.
In the 90s I worked on a lot of sampling projects - those went straight to SCSI HDDs & get copied [with data checksumming] as technical standards change... having learned the lesson once, it's not going to happen again.