I see a benefit to both methods and looking for experienced user preferred choice and why.
The Software Storage certificate is safely stored in the browser certificate store on your local PC or laptop and can only be used on a single device.
The Hardware Storage certificate is bound and stored on a FIPS 140-2 compliant hardware device (USB token or Smart card), and can be used with multiple PCs or laptops if they have the ActivID software installed.
I have an IdentTrust software storage certificate, although I do not use it for notarizations. (My state, Vermont, has not yet passed rules for electronic notarization or RON and I won’t be able to do those until rules are passed.) When the certificate is installed initially it is only on the computer where you downloaded it. But the normal practice, and what I was able to do, was export it to a file and import it into other computers and browsers.
I have read about how some of the RON platforms want to work with notaries: they want the notary to upload the certificate, and their secret key, to the platform’s computer and the signature will be applied on the platform’s computer, when the notary clicks the appropriate boxes. Or so they say; once you upload your secret key to them, you’re just trusting them to do the right thing.
If you order a hardware storage certificate, you would probably choose the USB token. To sign something, like a notarial certificate, your token must be plugged into your computer. The token is designed so it is impossible to export the secret key from the token. The actual math part of the signing process occurs inside the token; it doesn’t just have storage like a thumb drive, it has some computing hardware as well.
This means that the platforms that want to do the signing on their computer can’t do it, because there is no way to send the secret key to the platform. So the hardware storage certificate won’t work with some RON platforms.