email is hosted third party (think Outlook, Gmail etc.)
Is this more secure and "private" than sending en email to the same person, but with his/her email account on a different domain (as in above example, but now from [email protected] to [email protected])?
Assumption for this scenario (to reduce scope):
separate domains are not owned by related entities (going by above example, the relationship between the owners of example.com and anotherexample.com is as disparate as Microsoft and Google).
both domains' email servers support STARTTLS, and implement typical security practices (IMAP, SMTP connections from clients use only TLS, both accounts use strong passwords and servers store passwords properly hashed, salted and iterated, patching and configuration is done properly etc.)