MailMessage represents a whole MIME (.eml) or Outlook (.msg) message, while ImapMessageInfo represents a more-or-less complete information about the message retreived from the IMAP server (it does not contain attachments, for example, although it may contain information about attachments and message HTML and text bodies).
Unfortunately, we are no experts on EWS Managed API. It's also somewhat beyond the scope of our support - it's a third-party component after all.
However, we are currently working on an alternative to EWS Managed API - it uses the same Exchange Web Services API internally, but we aim to implement a Rebex-like API on top of it. A beta is available at Rebex Labs and although it's not yet feature-complete, it is already usable for a lot of scenarios. Perhaps you would like to give it a try?
UPDATE January 2016:
An alternative to Microsoft Managed EWS API called Rebex EWS has been released as part of Rebex Secure Mail 2016 R1. It features the similar API as our SMTP, IMAP and POP3 clients, so for people familiar with our mail components working with Exchange Web Services should be a much smoother experience. Download a free trial and give it a try.