Flipping through the documentation, the RESTful API seems to only allow for polling for new messages (deltas via the sync protocol[1]).
While I'm glad that there is a delta-API, I'm concerned that this doesn't support proper "push" notifications for new messages. This is a valuable feature of Exchange and IMAP[-IDLE](where supported).
I understand that the heterogeneity of these push protocols makes it difficult to expose a push API, but it seems an important feature of mail clients.
Similarly, it seems that REST is not quite the best protocol for the "push" piece of modern email. I suppose long-polling support on the Sync API would work fine, however.