CyanogenMod keeps most of the aesthetic and conventions as they are in stock Lollipop. It uses that as a base to build on top of and add customization options. There's even a Google Apps package that will install the stock apps and Google Now Launcher, but can be avoided if a cleaner experience
CyanogenMod includes the ability to define profiles that include a set of system settings. For example, a profile for home may include turning on Bluetooth, while a profile for Office could turn down notification volume. They can be switched manually or based on triggers such as location, when on...
MIUI has visual similarities to iOS and TouchWiz and combines functionality from both iOS and Android OS and its variants. For example, MIUI has no apps drawer and instead puts all app on homescreen pages the same way iOS does.
Xiaomi, the developers of MIUI are Chinese and their primary maket is China. As such primary language for most apps and services is Chinese and not all of them have yet been translated to English or any other language.