iCloud vs me.com address

You don't need to delete your iCloud account. Everyone with an iCloud account is receiving an @icloud email address but they aren't active yet (see second paragraph here: http://support.apple.com/kb/HT5441). You can decide if you want to use it or not; your @me address will continue to work. You set which account is your default account in Settings>Mail,Contacts,Calendars>Default Account (in the Mail section). For now, you'll want to keep the @me address as your default as the @icloud account won't work for a few weeks.

Hmmm.. you're the first person I've heard say that the address actually works now. Must have just started. But unless something's changed that I don't know about you still should only have only one primary iCloud account, and the others are just secondary accounts. Your primary account is the one listed in Settings>iCloud. The others are only listed in Settings>Mail,Contacts,Calendars. Secondary accounts will sync Mail (fetch only), Notes, Contacts, Calendars, and Reminders but only your primary account will sync Bookmarks, Photo Stream, Documents in the Cloud, Backup you phone and host your photo stream (see http://support.apple.com/kb/ts4020). Are you saying when you try to delete a secondary account it's warning you that it will delete your iCloud data from your phone?

I'm not doubting you, and thanks for telling me. I just hadn't heard that was working for anyone yet.

Both my @me.com & @icloud.com work.

I'm getting the same error on my iPhone 5, and when I turn off the ability to send from the @icloud.com address in settings, it only removes one and not the duplicate. Very annoying.

Okay, I have the solution for anyone still experiencing this problem...

Go to http://appleid.apple.com/ and delete the duplicate account from the 'Alternate Email Addresses' section. Then delete icloud from your device and log in again, and bam! Duplicate account is gone.

Hope this helps.