I just posted a review of Arkon Sports mega armband for Note 2 which obviously should work perfectly for Note 3 as well. What's unique about it - it's designed for Galaxy Mega, and it fits perfectly Note 2/3 with any bulky protective case (tested with ZeroShock case and triple zerolemon battery which is bigger than Defender).
http://androidforums.com/samsung-ga...mega-sports-armband-note-2-3-w-lots-pics.html
http://androidforums.com/samsung-ga...mega-sports-armband-note-2-3-w-lots-pics.html
