When comparing Messenger vs Mattermost, the Slant community recommends Mattermost for most people. In the question“What is the best team chat software?” Mattermost is ranked 6th while Messenger is ranked 74th. The most important reason people chose Mattermost is:
You don't need to rely on someone else's servers, you can host Mattermost on your own server.
Specs
Ranked in these QuestionsQuestion Ranking
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 Can be self-hosted
You don't need to rely on someone else's servers, you can host Mattermost on your own server.
Pro One-line Docker install
With Docker set up, you can install Mattermost with the following command:
docker run --name mattermost-dev -d --publish 8065:80 mattermost/platform
For other cases, installation instructions can be found here.
Pro Similar to Slack
Almost all features of Slack are available in Mattermost.
Pro Free - OpenSource
You can download and use it as free for self-hosted server.
Pro Mobile apps for android and iOS
Pro You can change theme
Pro Desktop app for MacOS, Linux and Windows
Pro Browser notifications
Pro Mark-Down support
Yes, it supports markdown.
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 No easy End-to-End Encryption setup
Con Features not available out of the box
Difficult to setup the many features it offers. The easy docker installation is for the application only, not it's feature sets. Requires a license for full-set of features.
Con Centralized
Con Poorly made iOS app
Built natively using React it suffers from unresponsiveness, input lag, and sometimes broken services. Coupled with a bad user experience.
Con Poorly made Android app
The Android application is just a badly wrapped web-view which does not perform well and has no form of offline caching whatsoever.
Con Self-Hosted
This doesn't work for every type of company. Mainly great for those concerned with privacy, security, compliance and control of your data/information.
