Asana is a very simple task management application. If you are looking for an application to store and track lists of tasks, it does it very well. Asana is very focused on lists and tagging. If you love GTD, it's going to deliver for you. Sharing is easy enough but assigning a task to a college requires you to type in their name each time. Once you get the shortcuts down, you can be very productive with it.
Trello has all that you can find in Asana with a very intuitive, easy to use interface. Trello follows a time honored tradition of establishing a "board" for your projects and placing cards on it in various lists or stages you define. It lacks the tagging capability that asana delivers. It lends itself better than asana to the concept of objects flowing through different stages or statuses -all of which you can define. It's very good for mapping out and establishing workflows in teams. Because of its layout, you can visually deduce bottlenecks and lack of work in different stages. Sharing is simple and assigning is even simpler utilizing drag and drop of people's faces onto the cards.
Both services are free.
Trello allows multiple Boards with simple and powerful security. Alternately Asana allows up to 26 workspaces.
