When comparing Messenger vs GroupMe, the Slant community recommends GroupMe for most people. In the question“What is the best team chat software?” GroupMe is ranked 49th while Messenger is ranked 74th. The most important reason people chose GroupMe is:
GroupMe has a built in function to read receipts.
Specs
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Pros

Pro Uses Facebook friends to create a contacts list
Allows communicating with anyone who's a friend on Facebook.
Pro Read receipts
Can see who has seen each message in group messages.
Pro Easy to share posts from Facebook
Integration with Facebook makes it easy to share any interesting posts from the Facebook timeline.
Pro Great UI
User interface of the application is clean, intuitive and easy to overview.

Pro Reads receipts
GroupMe has a built in function to read receipts.

Pro Great web client
GroupMe has an excellent web client that can be used to send and receive messages and manage groups from the desktop.

Pro IFTTT Integration
Allows sending messages from web services via IFTTT.

Pro Integrated calendar
It's possible to add location and time with reminders directly in the GroupMe app.

Pro Makes it easy to silence 1 or all groups
GroupMe has settings that allow muting a single group or turn off all GroupMe notifications from within the app.

Pro Does not require everyone in the group to have a smartphone
GroupMe can set up a custom phone number which allows people without the App to send and receive messages. This makes it easy to add anyone to messaging.
Cons
Con Lack of privacy
Messenger is owned by Facebook. Based on their privacy policy, this means that any information you provide (including messages sent) are used by Facebook to profile you and sell access to your data to advertisers.
Con Lack of end-to-end encryption
Secret (end-to-end encrypted) chats are only supported in one-to-one messages, and are not enabled by default, and the encryption has not been verified independently.
Con Drains battery fast
GroupMe, in order to have a constant connection which allows for notifications drains the battery of a device quickly, which is not ideal for a messaging app that one needs on time notifications from.
