Sorry to be late to the party. It would seem that the O365 Planner as of 2020 is far more suitable for integrating with an existing Teams instance:
- Does not require a separate login, and you don’t need to configure AD SSO with Asana
- While the boards/tasks view is still limited like Asana, Planner has colored flags you can add to tasks to suggest the idea of sections/categories, so the board can still be used for following tasks through the process
- The description field can contain lists and checkboxes, and the field can be displayed in the card view for easy lookup
If you’re already using Teams, I’d stick with Planner, because many IT departments like all apps to fall under one vendor solution and are hesitant to integrate with independent (although often superior) products.
That said: Since MS Planner looks and works SO MUCH like Asana, has Asana contacted MS about a potential breach of copyright? Planner wouldn’t even exist without Asana. And if MS invested money into upgrading Asana and integrating seamlessly with it, then they wouldn’t need their own development team.