From their GitHub:

Molly has unique features compared to Signal:

• Data encryption at rest - Protect the database with passphrase encryption
• Secure RAM wiper - Securely shred sensitive data from device memory
• Automatic lock - Lock the app automatically under certain conditions
• Multi-device support -- Link multiple devices, including Android tablets, to a single account
• Block unknown contacts - Block messages and calls from unknown senders for security and anti-spam
• Contact deletion - Allows you to delete contacts and stop sharing your profile
• Disappearing call history - Clear call notifications together with expiring messages
• Debug logs are optional - Android logging can be disabled
• Custom backup scheduling - Choose between a daily or weekly interval and the number of backups to retain
• SOCKS proxy and Tor support - Tunnel app network traffic via proxy and Orbot

Besides that, you will find all the features of Signal plus some minor tweaks and improvements. As with Signal, SMS is not supported.

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Molly is open-source just like Signal. But Signal uses Google's proprietary software to provide some key features.

To support a 100% free and auditable app, Molly comes in two flavors: one with proprietary blobs like Signal and one without. They are called Molly and Molly-FOSS, respectively.

Nothing is wrong with the main signal client but it's open source so it's healthy to have options. One of the benefits of a robust open source ecosystem.

Molly has lots of neat quality of life features, and let's you use the old signal local encryption.

Back in 2018, Signal allowed the user to set a passphrase to secure the local message database. But this option was removed with the introduction of file-based encryption on Android. Molly brings it back again with additional security features.

Molly connects to the Signal server, so you can chat with your Signal contacts seamlessly. Please remember to review the Signal Terms & Privacy Policy before signing up.

We update Molly every two weeks to include the latest features and bug fixes from Signal. The exceptions are security issues, which are patched as soon as fixes become available.

https://github.com/mollyim/mollyim-android#features

Data encryption at rest - Protect the database with passphrase encryption

Secure RAM wiper - Securely shred sensitive data from device memory

Automatic lock - Lock the app automatically under certain conditions

Multi-device support -- Link multiple devices, including Android tablets, to a single account

Block unknown contacts - Block messages and calls from unknown senders for security and anti-spam

Contact deletion - Allows you to delete contacts and stop sharing your profile

Disappearing call history - Clear call notifications together with expiring messages

Debug logs are optional - Android logging can be disabled

Custom backup scheduling - Choose between a daily or weekly interval and the number of backups to retain

SOCKS proxy and Tor support - Tunnel app network traffic via proxy and Orbot

It depends on non-free Google Play Services for push notifications, which puts you into a requirement to use an unmodified Google Android, which is potentially dangerous for a privacy app like this.

Anyways, when it comes to E2EE IMs, Matrix ecosystem is much better.