The Xiaomi Redmi 3 Pro runs on MIUI 7.3, which utilizes an Android 5.1.1 Lollipop core. MIUI is one of the most comprehensive customizations of Android. It has a big following in China where Google services are not accessible so Xiaomi refocused the ecosystem away from Mountain View's services. For those living elsewhere, there are various international ROMs, which come stripped from the Chinese services, in favor of Google's.
The lockscreen is fairly standard (time, notifications, a couple of shortcuts), but once you setup the fingerprint reader you'll rarely see it anyway. Still, the Wallpaper Carousel can put beautiful images on the lockscreen every 15 minutes.
The always-on fingerprint sensor proved quite accurate and can take the phone from sleep to homescreen pretty quickly (the lockscreen is bypassed). It's not as fast as some flagship implementations, but the speed is quite okay at about 1.5s.
MIUI has a simple philosophy - every shortcut, plus widgets of your choosing are dropped on the homescreen. You get a docked menu for the most commonly used apps and there's a search field in the notification area if you can't remember where you put a rarely used app.
The notification area has two panes. The first shows notifications (and the search field), swipe left and you get the quick toggles and the brightness slider.
The app switcher feels like it came out of iOS 6.0 - apps are represented by their icons, in a single horizontal row. No matter the screen size, you don't get to see a lot of apps at a time and you don't get to see a preview of the state in which you've left the individual apps. You can pinch zoom to switch to the standard thumbnail card view.
Themes are fully supported and several are available out of the box. You can download more, they change wallpapers, lockscreen style, system icons and font, sounds too.
By the way, Xiaomi's proprietary Search widget does a similar job as iOS's Spotlight system-wide search. You can fire it up by swiping up anywhere on the homescreen. The tool searches through your apps, music, email, settings, among others.