They are very different platforms, Signal offers on-device encryption if you choose to enable it, prompting for a password when starting Signal after rebooting the phone. It will also keep a quick lock option in the menu on Android phones so you can easily prevent unauthorized access.

I believe Whatsapp has made a few compromises in this regard, but obviously Michael Cohen didn't bother to use disappearing messages in Signal or encrypt his Signal DB, despite how easy it is to do.

This is a common misconception apparently, one that I've fallen prey to myself in the past. Signal removed the option to use the password lock and now uses Android's built-in lock screen functionality to provide auth.

That screen was never meant to serve an encryption role and Moxie recommends using Android's full disk encryption feature to ensure data confidentiality at rest.

You can also set Signal to ask for a password after a certain time.