I'm having this problem, too, on my Nexus 5 and Nexus 7 (2013 version) since the 4.4.2 update. I can read other people's emoji (from iPhone) but can't send. When I look in my sent box, the emoji are broken there (#&xxxxxx), too.
edit: appeard to be still working in my twitter app, but not the gmail app
It appears that certain emoji work and others do not, for example I tried a random set of 10-ish:
Those two in the middle are the working ones.
The "source" (go into gmail website and hit "original message" on the email) looks like the following:
Going to try to downgrade to 4.4 probably, if this doesn't get fixed somehow... or try CM.