From my review, it looks like Asana tries to "replace" your email, whereas TaskMail punts the problem of trying to get folks to move away from email and just works within the confines of your email inbox.

As a user of Asana at my old company, I think the this paradigm of working within email will ultimately be the way forward for enterprise + medium sized companies, as getting larger companies to move away from email is probably not happening anytime soon. Whether or not this move happens with TaskMail, or some other tool, remains to be seen.

As an asana user, I too would like a response to this.