I've figured it out! After much confusion re: a Macbook air's Airdrop that stopped working after a reinstall of OS X.
You need to do a few things in order to make this work on BOTH computers, the order of which isn't concrete and you may have to go back and forth but make sure all these boxes are checked:
1. Go to system preferences and go to "Bluetooth"
2. Make sure bluetooth is on and that is says "now discoverable"
3. Pair your computer with the other computer if you see it.
4. Go BACK to System preferences and now click "Sharing"
5. Make sure you check "Bluetooth Sharing" (you may need to do this prior to the other steps in order to pair the computer)
*I have also checked File Sharing as well, not sure if this would affect it but no reason to leave it off
After making sure all of these settings are the same across both computers I went back to my newer computer and in the airdrop window I clicked "search for older macs" and immediately both airdrops showed up and worked perfectly.
Hope this helps!