The Xiaomi Mi 3 comes with the feature-rich MIUI Browser. It does a great job browsing, syncing with your Google account, supports downloads, there is a night mode too. It is as fast as Chrome, but does not support Find on Page or copy text (only links).
The MIUI Browser turned less capable of handling pressure - it couldn't handle our battery-test browsing script for more than three minutes without crashing. That's why we suggest you install Chrome - just in case you need to avoid crashes or you need to find something on a page. Plus it can sync with your Google account easily.
The Xiaomi Mi 3 offers a great file managing app called Explorer, but there is no document viewer/editor pre-installed. There are plenty for free in the Play Store though (even ones made by Google), so this shouldn't be a problem.
The custom Calendar looks good, syncs with your accounts including Google, and offers Day and Month views.
There are also the standard sound recorder, notes, flashlight, calculator, clock, and weather apps, among others, that are a given in any self-respecting Android package nowadays.
By the way, you can activate the torch from the lockscreen by a tap-and-hold on the Home key.
When it comes to getting around, the Xiaomi Mi 3 relies on Google Maps and Navigation. Naturally, if Google Maps isn't installed on yours, you can get it for free. The app offers much of the same functionality as its web-based counterpart, although you will need a data connection to take full advantage of the navigation features. Street view mode with digital compass enabled is an especially neat thing that you should definitely check out if you haven't already.
Whatever you may be missing, you'll find it in Google's Play Store or Xiaomi's Mi Store for sure.