Microsoft has announced that a new version of ActiveSync is coming. This v16 is introducing a long waited feature request: synching the draft folder 
Also part of this new version, calendar items with attachment will be synched with the attachment.
At this time, this new version is being rolled out only on Exchange Online on a per user basic, not per tenant. This means you may have a user already using the new EAS version while another one may still use the “old” version.
To check the version, just use the Remote connectivity test from https://testconnectivity.microsoft.com/ by selecting Office 365\Exchange ActiveSync and look for the MS-Server-ActiveSync value (in this screenshot this is still version 15.1)
See http://blogs.msdn.com/b/exchangedev/archive/2015/06/08/announcing-exchange-activesync-v16.aspx