CyanogenMod is the only custom Android ROM with a for-profit company with a sizeable budget behind the product that ensures that the quality of the product is up to par with Android itself.
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 is preferred.
Compared to stock Android, CM12 gives a lot more control over user's privacy. There's a permission manager that can be used to prevent certain apps from accessing certain information, a blacklist for blocking any unwanted calls or messages for specified numbers and notification filter that can be used to remove certain apps from popping up in the notification area.
Lineage OS offers a more simple and less resource intensive OS option to those using bloated Android versions such as what is found on Samsung/HTC devices.
Main strength of CyanogenMod are the customization options that it brings to Lollipop.
For example, status bar items such as clock and battery can be customized, pending notification count can be displayed in the status bar, Quick Settings tiles can be reorganized. It can be set up to adjust brightness by sliding across the status bar or access Quick Settings by pulling down from the edge of the screen. On devices like the OnePlus One there's the ability to switch between onscreen and offscreen navigation buttons. Layout of the onscreen buttons can be changed.
CyanogenMod is good about keeping up the development speed. Security issues as patched as soon as new exploits are found and often devices can be updated to the latest Android version using CM months before a carrier issues an update.
After deleting delvik cache & formatting system partition, accounts, apps, & all personal preferences will be in place, as though the phone was just rebooted.
The main strength of Lineage OS is the customization options that it brings to Lollipop.
For example, status bar items such as clock and battery can be customized, pending notification count can be displayed in the status bar, Quick Settings tiles can be reorganized. It can be set up to adjust brightness by sliding across the status bar or access Quick Settings by pulling down from the edge of the screen. On devices like the OnePlus One there's the ability to switch between onscreen and offscreen navigation buttons. Layout of the onscreen buttons can be changed.
CyanogenMod has built-in weather information accessible from the Quick Settings and powered by Yahoo Weather. From there the weather information can be tapped to access a weekly forecast.
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 certain Wi-Fi networks or ner a specified NFC tag.
Installing community made custom ROMs such as Lineage OS there may be inherent stability issues. Enthusiast created ROMs have the potential to be wholly or partly unstable depending on the device and/or community.
CyanogenMod theme engine can change almost every aspect of Lollipops design. It evens allows mixing and matching parts of themes. Themes can be found via Cyanogen Themes Showcase or in the Play Store using the keywords "theme engine" and applied simply by installing them as an app and then selecting them in the the 'Themes' section of the Settings menu.
Brings features requested by the community for users to test. Relatively stable. An example would be bringing features such as the overhauled recents feature and heads up notifications from the Lollipop developer preview to Kitkat .
One of the most powerful theme engines, used widely among custom ROMs with a healthy amount of themes. Lets you customise almost everything on the ROM, including icons, colour schemes, framework layouts and bootanimation
Various services and apps require a Mi account. For example, buying new themes requires spending Mi currency that can only be obtained if a Mi account is available.
Xiaomi, the developers of MIUI are Chinese and their primary market 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.
You can customize these functions :
Theme Room
Palette
Decor Room
Tune
Quick Settings
Message
Notifications
Screen_lock_portrait
Lock screen
Web_asset
Status Bar
Whatshot
Xtra Options