Pros and cons of each?
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Google play has auto update, whereas f droid has semi automatic updates where it takes more effort.
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The Google play flavor comes with support for FCM (i.e. push notifications via Google infrastructure). The f-droid flavor relies on regular polling for events (so that messages might come in a little bit later, though I am not sure whether it can keep a connection open for real time push notifications).
The Google play flavor comes with support for FCM (i.e. push notifications via Google infrastructure). The f-droid flavor relies on regular polling for events (so that messages might come in a little bit later, though I am not sure whether it can keep a connection open for real time push notifications).
Edit: as the other commenter mentioned, since you are running google play services anyway, you can use the gplay version aswell.