Fastmail does one thing and does it well, email. There is no PGP support. Protonmail does PGP in the browser via a library that they serve you themselves which I find less than ideal. If you want to do it outside the browser you need to have a subscription and download a bridge software that needs to be running on your machine. With Fastmail if I need PGP in my email I do it via the GPGTools plugin for the Mail app which uses the system gpg installation.
Proton mail has more advanced cryptographic features and my understanding is that your email is encrypted so they can't offer it up to third parties without your consent (or at least stealing your password.) The usability is not as good: search often does not work very well (I believe this is due to the encrypted nature of it) and there are only a handful of local clients you can use via their bridge. The mobile app is pretty good, the web app is acceptable but clunky.
I use fastmail for day to day stuff I don't care too much about and protonmail for my more important/personal stuff. Both support custom domains so you can move your email to another provider if you get sick of one.
(Ex: I could search by the [Mailing-List-Tag] + date range, from address etc)
This is why I hope they fix the bridge: I'd like to index my email fully and locally, but I'm not going to use thunderbird to do it.
FastMail:
+ simple, lean, paid email.
+ fast web interface
++ working full text search( not just subject line)
+ No ads.
+ iOS App. Fast and simple.
+ Integrated calendar
- No encryption.
- group calendar has been a pain or non intuitive.
Protonmail:
+ Encrypted
+ Lean, safe web interface
+ IOS App that works.
+ or - Free as in cost.
- - - No Full text search.
- can't really configure your chosen email client to it...
- last time I tried, dragged and dropped images disappeared. May have improved UI now.
I only use protonmail for automated alerts and system originated communication.
Do you have any experience with using the IMAP Bridge? It is a daemon you run locally that translates between Protonmail's internal protocol and IMAP, to let you use your email client of choice. I'm using it and it seems to be working OK in my experience, but I don't use my Protonmail account heavily.