Recs.
Updated
SpecsUpdate
Pros
Pro Provides granular control over personal data
Compared to stock Android, Lineage OS 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.
Pro Mostly a stock Android experience
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.
Pro System profiles can be triggered based on set criteria
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.
Pro Lots of customization options
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.
Pro Customization options
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.
Pro Powerful theme engine
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.
Cons
Con Rooting a device may void the warranty
When rooting a device most manufacturers consider the warranty void, though returning to stock and re locking the device (if an option) before sending back to the manufacturer may hide that root ever took place. Though be warned as some devices keep track of if a device was rooted and returning to stock does not hide it.