I have an mxd with features from 2 geodbs added. When I try and move a feature I get the message 'The feature could not be moved. The spatial references do not match.' On closer inspection of the features in each geodb one has the features ticked for 3D

[RobBlackbourn]

Sorry first timer! The other geodb does not have 3D ticked. Also can not delete a new record I created as a test. See above!

[RobertBorchert]

Did you try to drag or simply copy and paste the feature class.  If the coordinate systems do not match it will not work that way.  The system needs to project the data into the new coordinate systems. 

Use the Feature Class to Feature Class to geodatabase tool