I'm going to expand a bit further as I gave their Outlook app a test run. But I guess you could say that this has to be the shortest lived app on my phone (less than 5 minutes).
First off, this is no different from their Hotmail app, as +Mike Wood
has pointed out. Whether or not it's less featured than before is unknown to me, as I was looking for 1 particular feature to be included.
That one feature that would let me keep the Outlook app on my phone is marking a selected mail as spam. You can't do that on the app. Yet you can do that for any selected mail via their web interface. This is the one thing that completely breaks the app's usefulness.
The UI could use work but that's not my place to really discuss nor critique. Making it look better is second to functionality and feature.
The app cannot be more useless than it is. Using it to access your Outlook/Hotmail emails is no different than using the stock Android email app and pulling the data via POP3. So why bother even installing it? Contact sync? Calendar sync? Both of which I don't even use. The real question everyone should ask is... "Is there a reason to use the Outlook app?" If I can't do all the things possible on the website using the app, it is not worth keeping or using. The biggest breaker is the inability to mark any mail as spam.