How to change the default Mail account in Mountain Lion?

Solution 1:

Instead of trying to drag the account(s) into the desired order in Preferences, drag the account's mailbox to the desired order from the mailbox list in the sidebar of Mail.app main window. Open the inbox and drag the desired sub-inbox to the top. The position in the other places like the trash and drafts boxes will follow.

Then quit Mail.app and open it again to make the changes take effect.

Whichever account's mailbox is at the top of the list will be the default mailbox.

If an account mailbox is at the top, but the account is not the default, drag it down and then back up to the top. This will reset the order and establish the top one as the default.