How do I share a shopping list between iPhone and Android?

Sharing in Apple Reminders needs an Apple Account on both ends. With Just List you share one link: on Android it opens in the app or the browser, nobody needs an account to join, and you both see changes live.

Can I get a reminder when I get to the supermarket?

Yes, in both. Apple Reminders does it on Apple devices; Just List does it on iPhone and Android, even with the app closed.

Just List vs. Apple Reminders

Apple Reminders is built into every iPhone, it's free, and its grocery lists sort themselves. The catch shows up when a list has to leave the Apple world: everyone you share with needs an Apple Account with Reminders in iCloud. Just List works the same on iPhone, Android and the web, from one link.

What Apple Reminders does well

Already on your iPhone, free, and synced across your Apple devices.
Grocery lists sort items into categories like Produce on their own.
Reminders by time or place (arriving or leaving).
In a shared list you can assign items to people and get an alert when something is added or completed.

Feature	Just List	Apple Reminders
Who you can share with
Who you can share with	Anyone with the link: iPhone, Android or a browser, no account to join	People signed in to an Apple Account with Reminders turned on in iCloud
Location reminders
Location reminders	✓ Arriving or leaving, on iPhone and Android, free	✓ Arriving or leaving, with an area size you set
Grocery list
Grocery list	Shared live, with a reminder when you reach the store	✓ A Groceries list type that sorts items into categories
Splitting up the jobs
Splitting up the jobs	For events: guests claim what they bring from a link, no account	✓ Assign an item to anyone on the shared list