If you're both on iCloud-enabled devices (big "if" unfortunately), Apple Reminders actually works great and is quite seamless. It's fairly easy to set up and link lists together — you don't need to sign up for new accounts or install another new app (which is a hard sell for people sometimes — not everyone wants to sign up / download Wunderlist and check it all the time). I think you can even link up lists using Airdrop. You can use Siri to create reminders and interact with them. Plus third party apps can easily integrate with Apple Reminders (e.g. Grocery https://www.producthunt.com/post...
). It's also simple and easy to use.
It'll also automatically sync your list changes to iCloud so if you have a Mac or you login at iCloud.com you can add new reminders there.
Similarly with Apple Notes etc.