There is a chance that the birth date on either or both records is incorrect.
Usually it is a survivor, not the decedent, who arranges to have a headstone carved so it is not unusual for the survivor to make a mistake.
I have no knowledge of German birth records, but if one is available, try to get the birth certificate. If your ancestor married, the birth information may be on his birth certificate.
Try posting on the appropriate Germany board for help with German records.