Everything runs on RAM and will disappear the second a server is shutdown, they really don't store anything.
And you can buy a Mullvad account by mailing cash to them or with crypto. No need to create an account with an email address or anything.
This quote is in reference to ProtonMail in 2019, a fairly widely reported on case at the time.
This would be a point in favor of Mullvad, as Mullvad has demonstrably squashed a subpoena in the past, thanks to their data-minimization policies (no PII for signup, no PII options for payment, diskless infrastructure, etc.).
Note that this is more related to privacy, and not as much security. If the parent comment was specifically talking about security, I would recommend reviewing the software and infrastructure audits made available by either company. I'm not aware of any major fault with either, from a security perspective.
You can find many articles about it (search "Protonmail subpoena 2019"), but an example article is here: https://www.privacyaffairs.com/protonmail-surrenders-user-lo...
ProtonMail's own blog post about it is here: https://proton.me/blog/climate-activist-arrest
That being said, Swiss law is very restrictive, and there are a lot of hurdles that one needs to jump through to get a court order. And even with a court order (and has been proved multiple times in court), there is no way to break Proton Mail's encryption. Privacy is not the same as anonymity, and due to the way the internet works, if anonymity is what you are going after, you have to exercise proper infosec and take preventive measures, such as using Tor or VPN.
Under Swiss law, the treatment of VPNs is different, and VPNs can indeed be no-logs, like Proton VPN is. No-logs VPN is also possible in other countries as well. What makes Switzerland different, and possibly unique, is that within the current Swiss legal framework, Proton VPN also does not have forced logging obligations. You can find out more here: https://protonvpn.com/blog/transparency-report/.