I do disk drives, and have for the last 20 years or so.
Practically speaking, unless you have a government actor or someone with extremely deep pockets coming after you, just wiping a drive once is enough for privacy.
Not practically speaking, and assuming you're worried about a government-grade attack on your drive, a single write of a constant value or a psuedorandom pattern that I can predict isn't enough to completely erase the data. Heads are always slightly misaligned from the servo track, so there's always some leakage at the edges that usually survives a wipe, although it's usually -20 dB or so down from the main signal and requires some finesse to get to. It's this misaligned head that's the most practical attack on erasures. Then you can go to more exotic things (transition modulation, etc) that are less likely to work.
There's also a problem with abandoned sectors in your drive leaking data. What we do in modern drives is that we have multiple tracks that we use for backup data. When a sector starts to go bad and we have to do multiple retries to read the data (including some very, very weird read modes), we'll take the data and move it to a backup track, then mark the original sectors bad, while mapping the new sectors into the file system so that everything is transparent to the user. You'll never see this, it's all done behind the scenes in ways you can't detect. So the old sensitive data is still there, but hard to read, and nothing you do as a user can ever get to it.
But all these weird modes are HARD to get to, and the data recovery is often pretty manual and extremely expensive so unless you're Edward Snowden it's not worth the time of the NSA or DoD to come after you.
So my view is pretty simple: single pass erasure for normal business users or personal use, although I tend to do erasure and a reformat to a completely different filesystem type (e.g. to ntfs from ext4) if I'm giving an old drive to a friend/relative. Usually I take my old drives to the shooting range for destruction just because it's a lot more fun. If the data is really, really private where not one bit can afford to be found, then shred it. It's not like disks are super expensive.