MIME is the standard format used by most email clients and email providers except for Microsoft that uses the MSG format. The MIME format is based on several standards (RFC 2045, RFC 2046, RFC 2047, RFC 4288, RFC 4289 and RFC 2049). It has been created in 1991-92 by Nathaniel Borenstein and Ned Freed. In 1993 the MIME format was blessed by the IEFT (Internet Engineering Task Force) as a draft standard.
Because it is a standard, you can't go wrong when using MIME for saving your email. The disadvantage of this format is that links to external images will probably no longer work in the long run, meaning that you might not be able to see the complete email.
The MSG format has been created by Microsoft, who owns the intellectual property rights. It is based on the Compound File Binary Format which, as they describe it, is similar to an FAT file system within a file.
Microsoft Outlook is the only product to use this format. The MSG format specification has been released on 2009.
It is widely used because of the popularity of Microsoft Office in the workplace worldwide which had been unchallenged for years until alternatives like Google Docs became popular.
I would not recommend using this format for new backups unless you use MS Office and plan to keep using it. The external images linked in the email can also be lost in this format.
The PDF format (Portable Document Format) was created and conceived for presenting documents in a manner independent of application software and operating systems. It was developed in 1990 by a team led by Randy Adams as a way to share documents and images between disparate systems. Its specifications were proprietary to Adobe until they released them as an open standard on 2008.
Because it was designed to be universally available and independent of the computer where it is used, it has become hugely popular and has become the standard for archiving documents.
It is the preferred format for email archiving because the external images can be included in the document and can be displayed as the original email.
Rich Text Format RTF
The Rich Text Format is proprietary to Microsoft and has been used for cross-platform interchange with Microsoft products.
Use this format if you need to export your email to MS Word.