Sorry to bump an old thread but was this every resolved for anyone? I still have tons of problems with emails syncing between Outlook.com and WP8.1 on my 928. Deletes on the phone are mirrored correctly on Outlook.com but deletes on Outlook.com do NOT delete the same emails on the phone. Here's what I've tried to rectify this:
Manual sync on phone - no effect
Changing the Hotmail server on the phone as suggested above - no effect
Soft reset - no effect
When a new email arrives on Outlook.com, it is correctly pushed to the phone but the old deleted emails still remain on the phone so a general sync does not happen so - no effect
Changing settings from "as items arrive" to "based on my usage" to "every 15 minutes" etc. - no effect
The ONLY way I can get email to sync is by going into email and account settings on the phone, selecting the Outlook.com account, unchecking 'email' as an option that syncs with the phone, wait for WP to delete all the email, then go back in and recheck 'email' as an option to sync, wait for WP to resync all email for that account, and the emails deleted on Outlook.com are finally deleted on WP.
I've left emails on WP that I deleted weeks ago on Outlook.com and they never, ever get deleted on the phone. So I'm not talking about emails not disappearing immediately after being deleted on the web.
Anyone have any other suggestions? A search on here seem to point to thread with people having calendar and contact syncing issues but very few threads related to email syncing.