FastMail chooses not to mine your data (even for spam filtering, they only optionally collect emails you permanently delete from the spam folder). They're a paid service, with no advertising. And they have a very strong privacy policy.
ProtonMail encrypts your email storage in an end-to-end manner for client access and storage. (Obviously, unencrypted mail sent to or from other servers could be intercepted.) But their goal is essentially to be mathematically unable to view your email. Of course there are tradeoffs, things like IMAP don't work (without some sort of relay), for example.
Essentially, FastMail makes a point to not violate your privacy, ProtonMail tries to make it so it can't violate your privacy. I lean towards FastMail because it's 'good enough' on privacy, and has a lot of powerful features, but if you're looking to run afoul of state intelligence agencies, you might wanna lean for the latter.
