My more detailed comparison of features can be found at the link below (don't forget to open the notes attached to some cells). But what I can summarise very high level here are some of the key indicators that many may use to make a decision. They are both very secure and it is your own use case that may sway you one way or the other. Both companies have ZERO access to the content of your mail so if you forget your password and recovery codes, that's gone (which is as it should be). Both have mobile apps for iOS and Android from free tier.
Tutanota key points:
* Double the free storage, as well as half the cost at the 10GB storage level. They claim compression could give more space.
* It has an encrypted calendar in the free tier.
* It has secure full text including content search.
* Subject lines encrypted by default.
* Both U2F and TOTP authentication.
* Does not support OpenPGP (they say because the subject line is not encrypted and there is no support for Perfect Forward Secrecy).
* Lot of recent availability issues due to DDOS attacks against them.
* Has proper desktop apps for Windows, Linux and Mac to sync mail offline.
ProtonMail key points:
* Does cost more. Free tier only 500MB storage.
* Calendar only in paid tier.
* Can only search addresses, date, subject line of mails. May be getting full search in future.
* Thunderbird with Enigmail will send encrypted subject line mail to ProtonMail fine, but for sending from ProtonMail it does not encrypt the subject line. Receiver can read the OpenPGP encrypted content fine.
* Reputation for stability and mitigating DDOS attacks.
* No desktop apps. Paid tier has ProtonBridge IMAP/SMTP which will allow Thunderbird and other clients to import/export fully encrypted mail.
So to really use encrypted mail effectively you probably either need to pay or consider privately hosting your own mail server with something like Thunderbird and Enigmail which will encrypt it for you (own hosting also costs usually).
See more details at CryptPad