Since the early 90s DD and HD floppies were made with the exact same media inside.
But: once these get written to with a HD drive (e.g. PC preformatted) they may be troublesome in DD drives. According to several experts, HD heads write 'harder' bits that are just overlayed with the 'softer' DD bits. The DD bits deteriorate faster than the harder HD ones and practically get overwritten from underneath. This effect depends largely on the exact specs of the media used (which we usually know nothing of).
I can't confirm this from my own experience though (been using an Amiga HD drive for the last 15 years), but for valuable data it's definitely worth considering. Actually I don't trust floppies further than I can throw them...