I really like this new Outlook app. The only thing that makes it a non-starter for me is that it doesn't properly support Gmail aliases. I have yet to find any third-party app on iOS that does support Gmail aliases fully except for the actual Gmail app.
What I mean is that when I configured aliases in Gmail, I set them up to use custom (i.e. not Gmail's) SMTP servers. The primary reason I don't use Gmail's SMTP servers with my domain e-mail aliases, ironically enough, is because the Outlook desktop client will display the From field like this if I use Gmail's SMTP server:
abc@gmail.com On Behalf of <My Name>
Since most of my clients use Outlook on the desktop, I want to present a polished image of my organization and not show them my personal Gmail address in the From field.
I'm not sure why e-mail apps other than the Gmail app can't access my aliases and their SMTP settings when I give them permission to access my Gmail account.
All the third-party e-mail apps I've linked to Gmail (Sparrow, Mailbox, Outlook, etc.) make you add your aliases to the app manually and then after you do that, it doesn't check to see what your custom SMTP settings might be for the alias -- it just sends all the mail using Gmail's SMTP server and gives you no ability to modify that behavior.
The Gmail app is the only one I've found that as soon as I gave it my credentials to login, all my aliases were automatically populated and when I sent an e-mail from one of my aliases using the app, it automatically respected the SMTP settings I have configured in Gmail on the web.