The German Corona-Warn-App is unique because
- the code is open source,
- there is no obligation to install it, and
- central data processing is limited to what is necessary to inform people who might have been in contact with an infected person; only the Temporary Exposure Keys are send from the phone to the server in case a person identifies himself/herself as being infected.
I think no other government in the world has this open and voluntary approach. To support the experiment, and of course if there is a chance the app would help to trace infection chains, I believe it's worth to install it. Unfortunately, my phone is six years old and doesn't support the version of iOS necessary to run the app. I'm on iOS 12.4.7 and at least you need 13.5.
I've heard such an app would only make sense if 60% of our population use it. That's difficult. The only app with such a widespread use in Germany is WhatsApp. But let's see how it goes. I think it's worth installing.