You're in control of all deliveries to you, so you can grep through your logs and see any and every delivery attempt, which you can't do with, say, Gmail.

You can store your data however you like, with as many (or as few) security considerations as you please. Want full disk and OS encryption with a Yubikey that has to be physically present when you boot the system? Sure! Want to encase it in a cube of concrete? Install your server at the top of a tree? Why not? Want to store all of your email encrypted in memory? Go for it!

You can back it up as you like, you can make sure nobody else sees or indexes it, you can access it via command line, webmail, IMAP, POP, whatever. You can more (less) your spool file directly. You can overwrite the disk where the mail was stored when you delete it. It's up to you.

Smarthosting does mean you have less control at delivery time, though. For instance, I can choose to refuse to deliver email to domains that don't negotiate TLS. Smarthosting doesn't easily allow this (or at least I don't know of any way to do this).

But every other part will still be 100% in your control.