I initially had my airdrop set for "contacts only"...my co-worker had his "contacts only"...we are in each others contact list.
my 5S recognized his 5S...but his would not see mine
we switched both to "everybody" and airdrop worked
I also had this problem....then noticed that if I put the other parties Apple ID email address in their contact info, they appeared. It doesn't recognize phone numbers associated with the accounts for some reason.