Fax is in no way more secure than e-mail. Once it's doing VOIP over the Internet, you have no more idea how secure or not the transmission is than an e-mail. Fax itself has 0 security. In fact, you can and people used to just tap the old phoneline and read the faxes. The "security" was you had to get into a place to tap the phone line you were interested in, but again, probably close to 0.1% of phone calls go over traditional phone lines today. And a large percentage aren't on isolated carrier networks either, but straight up VOIP on the Internet.
Worse, it's about as easy to "steal" a phone number as an e-mail address and just receive the faxes directly.
If you care about security, there's no standard I'm aware of to secure fax at all. E-mail has SMIME and PGP standards that can be used so that even if you intercept the e-mail or steal the credentials or hack the e-mail server, you can't read the messages without the local keys on the recipients computer.