Your files are stored in its memory blade "drive", which you probably transferred to your new board. But your old board will have your wireless network key saved. If you are concerned about its next owner "leeching your Wi-Fi", then you need to
zap its pram reset NVRAM.
2017-03-20 edit add:
Yes, wireless network key is
almost all I can think of. There are two other things which a disowner needs to take care of (which I withheld mentioning for no good reason).
firmware password (If enabled, then logic board is as good as a "brick" to next owner.)
Serial number. If you registered ownership, or associated it with your Apple ID, then you should un-register, unlink, disassociate your old logic board serial number from your accounts. I do not know how large is this can of worms. It might touch iTunes DRM, App Store DRM, iCloud Lock, Find My Mac, or other features which I do not know about. (These are features/antifeatures which I never will use.)