MarcinCzaban I've done a little bit of testing with the Outlook app from time to time just to stay current on what MS is up to with the app and in my experience its some times faster then Boxer other times its on par with it. Boxers FastSync feature is pretty awesome if you haven't tried it yet but ultimately both platforms are cracking down more and more on background syncing apps so I think third party apps are always going to be battling to keep up with the speed of native apps.
One thing to do on Android is make sure users have turned off the battery optimization feature as Android's algorithm well cause a pretty big delay if the user is not a heavy user of their mobile mail client since it looks to see how much and how often you interact with each app so if they are not constantly using it the it will push it way down the priority list.
Also in regards to ENS for the Outlook app its my understanding (someone correct me if I'm wrong) but Outlook Mobile app runs over Exchange Web Services which ENS runs over that as well so if you have used the Hosted version of ENS I'm going to guess the Outlook Mobile App has MS version of that built into the app that gets pushed by default based on your exchange server where as VMware/WS1 has you add a specific line to the config since they are not the actual Mail Server.
VMware Boxer’s new FastSync tech could usher in a better third-party email experience
