The free outlook.com only supports POP, IMAP, and ActiveSync (which is m.hotmail.com).
The mid to high tier Office 365 plans provide Exchange access.
The company that makes the mobile app Touchdown has a third party mail app that supports ActiveSync for OS X. But for Mac Mail, there is no ActiveSync option.
Office 365 works fine on OS X. You don't need a 3rd party app. It connects using EWS instead of ActiveSync.
Outlook.com connects to Windows (desktop) Mail via "DeltaSync".
Currently, there isn't an email client for Mac that supports it.