tldr- they both seem to be very secure email providers, with some differences. To fully grasp differences, read the links referenced below.

I've done some research, but not much. I should have researched more before speaking, so if I'm wrong, please let me know! I just want to have the most secure email. Anyway... here are a few things I've found. I'm no security engineer, so others may have more insight.

First thing is the location of the datacenters. Protonmail's servers are apparently under 1000 meters of solid rock in a bunker, and they claim it could even survive a nuclear attack. (And, they aren't in the US) (https://protonmail.com/security-details) Even if that's there for marketing purposes, it's kind of cool.

To compare, FastMail also has good security, but it's based in New Jersey, and I don't think it could survive a nuclear attack ':) (https://www.fastmail.com/help/ourservice/security.html)

That stuff is important, but unless something crazy happens, I doubt there is going to be any serious physical attacks on the servers. But, you never know.

ProtonMail is open source, and I know some of FastMail is too. Not sure if it all is or not.

ProtonMail has end-to-end encryption, and while FastMail has encryption, it's not 100%, and on the above /security.html link, it seems employees have access to some data, and full encryption is still a work in progress.

From the link: 'At this stage, some system log data (which could contain personal information) is temporarily stored on un-encrypted disks on individual servers, however we have an ongoing project to bring encryption to all system logging as well.'

Probably the biggest thing is when a company is forced to hand over data. ProtonMail keeps a Transparency Report, so the world knows about everything dealing with this. (https://protonmail.com/blog/transparency-report/)

ProtonMail is under Swiss law, and FastMail is under AU law. They both claim to not answer to US claims, but FastMail does have servers in the US, so I'm not sure how that all works.

Anyway, you can read more on their sites from the links provided. Hopefully some of this was helpful.