If you're asking about Trello - then I see one big difference - Trello has way simpler interface - to the point I could send my boss and colleagues invites and they immediately knew how to use it - whereas even my most geeky friends had problems figuring out how to use Wave (I did too.).

They seem completely different to me. GWave is a collaboration/communication tool. Asana is a project management/planning tool. In theory you could do PM with GWave but it would be a bit of a stretch.