App store or Google Play?

Is there a way to generate a QR code that will open either the Apple App Store or the Google Play store depending on the device used?

Yes, this is possible. You can connect a short link to your QR code and then in the settings > Targeting of the short link you can set different destinations based on the operating system:

First, go to the tab "Targeting" and then choose the targeting type "Operating System" this allows you to add multiple operating systems and the destination per operating system. When the user's operating system is not in the targeting list it will take them to the initial destination.