Which one should I pick for a new project?

I can only make a recommendation based on what these libraries do—they serve entirely different purposes:

google/exoplayer is a media playback library for Android. However, it is deprecated and no longer maintained. The README explicitly states [google/exoplayer README.md:L3-L12]:

This GitHub project is deprecated. The latest version of ExoPlayer is published as part of AndroidX Media3. All users should migrate to AndroidX Media3... As of 2024-04-03 we have stopped pushing commits to the dev-v2 branch in this repository... exoplayer:2.19.1 was the last artifact released from this project, we don't plan to release any more.

For a new project requiring media playback, you should use androidx.media (Media3) instead.

karumi/dexter is an Android runtime permissions library. However, the README notes [karumi/dexter README.md:L7-L8]:

This project is no longer under active development. If you are looking for an Android library to be able to request Android permissions in runtime take a look here

For a new project requiring permissions handling, consider modern alternatives recommended by the Android Arsenal tag referenced in the Dexter README.

Bottom line: Neither library is recommended for new projects—both are deprecated. Use androidx.media3 for media playback and modern permission libraries (or the built-in Android permission APIs) for permissions.

FOLLOW_UPS:

• What is androidx.media3 and how to migrate?
• What modern Android permission libraries exist today?
• Can I still use these libraries if already shipping?