Solid state disks are definitively to be preferred. Note that they are not without their troubles either, since sometimes implementors just suck (and Windows/Bitlocker sucks, too).
Traditional disk drives have been "encrypting" (or rather mixing) data weakly since pretty much forever to distribute bits better, but this doesn't help much in protecting data. More recently, there exist harddrives which are self-encrypting disks (SED), but as harddisks they are kinda "prestige" products and outrageous in price. I haven't so far owned one.
Solid state disks are practically always SED, but the feature set, and more importantly, the quality of the implementation differs a lot. As you can read in the linked article, for example, earlier models from Crucial used an encryption that was total bollocks. The user's password is compared to a hash by the firmware to "unlock" the drive's encryption key as opposed to e.g. Samsung's drives which use PBKDF2 to derive the key from the password. Which, in terms of actual versus misleading security is worlds in between.
Luckily, in any case, and regardless of bad implementations, the security-while-used is much more affected than the security-after-erased. Well... luckily, I don't know if that's a good wording, actually systems should always be secure. But at least it doesn't suck beyond.
There exist the notion of "master password" in the ATA standard, so any such thing as unlocking verus deriving an encryption key is -- even not considering that someone might find a way to read out the storage -- catastrophic. It basically means nothing is encrypted at all in a meaningful way.
Secure erase on a SED means erasing the disk encryption key, rendering the contents of the complete disk unreadable. So, unless one assumes a maliciously-built drive (which tells you it did a secure erase, but secretly still holds a copy of the key), this is secure even in presence of a broken implementation, and even in presence of someone cracking open the controller chip or such.
Secure erase on a traditional harddisk means the disk will overwrite every sector. I've recently done that with a pre-fail (SMART showing errors) Seagate Barracuda that was to be RMAed.
And guess what, secure erase is all nice and well, but a pre-fail disk will simply refuse to do the job. It'll start, whack around for a few minutes, and terminate with "error blah blah" after erasing approximately 10% of the disk. That wasn't an issue in my case since the data on the disk was from a RAID with software encryption on top, so any contents was basically useless anyway (wiping not really necessary). But, you get the idea. If you didn't use an encrypted filesystem, there's now no way to erase the data!
Generally, wear-levelling (both on traditional disks and SSDs) may make overwriting stuff much less possible than you are maybe inclined to believe.
Also, restoring overwritten data on a magnetic disk is possible. Yes, it is much, much harder than it was 15-20 years ago when data density was much lower (back then, it was pretty much a routine job). But it is still... generally possible.
So, if the data is truly super-sensitive (as in medical records), either one should layer software encryption on top, which eliminates the need to wipe the disk (though it doesn't hurt to do it anyway), or one should not donate the drives but use one of these to be sure.