A good comparison of the two can be found on PrivacyTools. Protonmail comes out on top because:

• ProtonMail accepts Bitcoin in addition to accepting credit/debit cards and PayPal; while Mailbox.org doesn't accept Bitcoin or any other cryptocurrencies as a result of their payment processor BitPay suspending operations in Germany. However, they do accept Cash by mail, cash payment to bank account, bank transfer, credit card, PayPal and couple of German-specific processors: paydirekt and Sofortüberweisung.

• ProtonMail has zero access encryption at rest for your emails, address book contacts, and calendars. This means the messages and other data stored in your account are only readable by you. On the other hand, Mailbox.org allows for encryption of incoming mail using their encrypted mailbox. New messages that you receive will then be immediately encrypted with your public key. However, Open-Exchange, the software platform used by Mailbox.org, does not support the encryption of your address book and calendar. A standalone option may be more appropriate for that information.

• ProtonMail is accessible via Tor at protonirockerxow.onion. When it comes to Mailbox.org, you can access your Mailbox.org account via IMAP/SMTP using their .onion service; however, their webmail interface cannot be accessed via their .onion service, and users may experience TLS certificate errors.

There's more that's compared on PrivacyTools' page, I encourage you to read it all.