Are you not just clicking off the composing window? Do you get a message saying this draft is being edited in another window? Apologies if not the case, just trying to understand the problem.
I would take Outlook over mail every time, with the one feature missing, that of not being able to disable an account which is useful for holidays etc.
I have had this same problem while composing an email, or replying to one, it just 'blips', and the email I was composing just disappears, and usually the email I was responding to disappears as well. I was using that email address to handle emails from subcontractors, and lost an email I had to retain as I was trying to respond to it. The system just blipped out, and I went looking for the 'draft', and not only was there not a draft of that email response in process as has happened earlier but the source email I was replying to was completely gone. Not in trash, not in draft, it just freaking totally disappeared. I wrote to their support and have heard nothing sense, and have stopped using Outlook. This was the outlook.live.com site. That kind of behavior is totally unacceptable, and not getting any responses from support is such a great feeling. And this issue just happens at random too making it a rich and fulfilling user experience.
I used to love outlook, but now avoid it like the plague. Hard pass...