When comparing Titanium Backup vs Greenify (Donation Package), the Slant community recommends Titanium Backup for most people. In the question“What are the best ROOT apps for Android?” Titanium Backup is ranked 2nd while Greenify (Donation Package) is ranked 4th. The most important reason people chose Titanium Backup is:
Can sync backup files to online cloud services such as Dropbox and Box
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Pros

Pro Schedule sync backups to the cloud
Can sync backup files to online cloud services such as Dropbox and Box

Pro Manipulate apps in batches
Can backup, restore, uninstall apps in automated batches.
Pro Hibernate overly active apps to save battery
Greenify's mane function is to hibernate any installed apps. This allows users to to quell overly active apps that are draining their battery without having to delete them. This can be done with or without ROOT.
Pro Even works without ROOT
Greenify even offers battery savings to non ROOT devices, though it may be limited compared to what can be done with ROOT and Xposed.
Pro Has extra experimental features over the free version
The Greenify (Donation Package) has a few extra experimental features that the free version does not offer. They require ROOT and the Xposed module to be installed. Using these features can help with the compatibility of the rest of the Greenify app, which is a big plus.
Cons

Con UI feels very outdated
UI is outdated, but it works.

Con Requires premium seperate app to unlock a lot of the features
Costs $5.99 to unlock features with separate unlock key download.
Con Greenifying without ROOT has to be done manually each time
When using Greenify without ROOT access to hibernate apps, it has to be done manually each time. There is a widget and shortcut that users can set to their home screen to make this action a bit easier though.
