Using outlook 2010 or 2013 is the most amazing experience but sometimes it can create problem. The same problem I faced when I sent a business message to a user of the same domain using outlook for mac and every time that user got the message in text format while I was sending the email in HTML format.
This problem can occur if you have saved the contacts in your address book and configured the message format for individual users. While creating the contact in the address book if you have saved the settings for that user in plain text. they will remain plan text even if you choose the HTML format while sending it that recipient.
The resolution given on the Microsoft website is not very much helpful because that only addresses to change the settings. please check the under given URL from Microsoft website
By following the the options given in the above post from Microsoft website you will only waste time.
The way I resolved this issue was simply delete the contact from the contact list and create it again with carefully choosing the HTML format from the message format settings.