The Outlook.com app for Android supports checking email from multiple Microsoft email accounts from all their services: Outlook.com, Live and Hotmail. Like the webmail interface, the user interface is extremely simple and flat. Email text is displayed with almost no formatting. I found it useful enough to read plain text emails, but that is about it.
Tried with: Outlook.com 188.8.131.52.49.7090, Android 4.4.3 and Moto G