As a long time, 'power' Asana user I can confidently say that it's a good task list manager and nothing more. "Project Management", or rather, at a higher level, "Work", is much more than a dynamic, shared, list of tasks.
Asana has tried to create the killer app, the email beating, unified metaphor for project management and... it's not enough. I would not have invested without a very promising roadmap.