I've read over the years that DD floppies are higher quality than HD floppies, but with the drives it's the other way round.
Hence, an HD drive will read and write HD and DD no problem, but a DD drive will read and write DD, but may struggle with HD.
From this I understood it was always better to buy DD floppies and they will last longer even in and HD drive.
Of course this coudl be total nonsense, but it is what I read and seems to make sense that as drive technology improved, the media didn't need to be made to such a high standard (expense).
I think the info you were given might be incorrect. From what I understand, the difference between DD floppies and HD floppies is not that DD floppies are "higher quality", but that they have a different formula of magnetic particles coating the disk surface - i.e. particles with a different magnetic bias than HD floppies (i.e. so they take a different strength of magnetic field to charge).
HD floppies have a particles formulated so they can hold higher density data despite the fact that they are using much narrower tracks and sectors. I'm guessing this "HD formula" requires a higher magnetic charge to write to and the particles are more "tenacious" (i.e. holds onto its polarity well despite a smaller area being used).
So from what I understand, the HD floppy drives can sense which disk is inside it (DD or HD) via a sensor pin that detects the presence / absence of the extra hole in the floppy casing, and so it alters the magnetic bias of the head to appropriately read/write to the type of disk that has been inserted.
Now....SOME DD drives don't seem to care that there when an HD floppy has been inserted. Obviously, with no sensor pin for the "HD hole" they can't know what type you've inserted. I've found that MOST DD drives will still happily read and write to a HD disk (except the one from my A500 mentioned previously). The danger, is, of course that if they DO write to an HD floppy, the drive head is not calibrated to put out the proper strength magnetic field for the "High density" particles. So, while the particles on the disk surface MAY be altered by the drive head, and the floppy may even work for some time, the particles are more weakly charged than they should be, and the disk may fail in weeks or months.
Alternatively, if you use a double density disk in an HD drive, and somehow cut out the extra notch so that he HD drive thinks you have inserted a HD floppy, and then format that disk to HD format etc. then again the magnetic bias is not matched to the particles on the disk surface - and I am assuming that since the HD bias is probably stronger, the particles on the floppy would become over saturated, and you would get reliability problems as well, if it held data at all without corrupting adjacent tracks.
Now, if you use a DD disk in a HD floppy, and it has the appropriate notches to identify itself to the drive as a DD disk, then the drive will adjust the magnetic bias of its head to appropriately read and write to DD floppies properly (as if it was an old Double Density drive).
It's like the old case of cassette tapes: regular Ferric Oxide standard quality cassette tapes and CrO2 high quality tapes, and even higher quality METAL tapes. You had to flip a switch on your recorder marked "bias" to signal to the cassette recorder what magnetic strength to use when recording. Some more expensive cassette recorders could sense by the notches in the cassette's casing what kind of tape had been inserted. But again, if you used the wrong bias on the wrong type of tape, the quality of your recording would suffer. With an analogue signal, usually you could still hear something - although it might be more or less noisy / distorted.
Anyway, this is how I understand it. If anyone can correct me or set me straight, feel free.
Now, as for DD floppies being "Higher Quality" --- well, they may be less likely to fail. I could see that. But I think that would be the result of the data being less tightly packed on the disks. The tracks and sectors have more room to "play" (further apart) and slightly mis-alignments in a drive's head (or from drive to drive) are not going to cause errors as much as where the tolerances are higher (on an HD disk, for instance). I've always found my old 1541 drive on my VIC to be very reliable - and thought that this might be one reason for that - only 360K or something per side. So maybe the lower read error rate of lower density media gives the impression they are "higher quality" to some.