I imagine a point that if coded with a point number, say "Column Center #100" would find point #100 in the drawing and would lable a North and East offset distance to that point. We would use this for all kinds of as-built drawings and boundary corner surveys.
I don't think you'll get a point with the ability to have two sets of coordinates.
As an alternative you might be able to create a line between the original point and new point then lable that?
Maybe use the survey import to define each point as a start and end for a survey/feature line. Then label the resultant using an expression to show the change?
I don't believe you need a point with two separate coordinates, what you need is the ability within Label Expressions to access points within the drawing or survey database. Then you could have Label Components such as N-Delta and E-Delta which can be formatted added into the Label Style.
I've done my share of As-Built Surveyor's Reports for pile's and pile caps. That feature would also be very benificial for Boundary Survey's as id would allow us to automatically label property corners and Fence coner relative to property corners.
I have attached a Drawing called Delta's which have label styles set up with Expressions to label delta's for lines. I use these lines/labels to call out differences between Calculated Property corners and Found Monuments.
To clarify I was understood that you may want a number of points to be displayed relative to one refference point hence the suggestion of an alternate coordinate system.
This can be done using the transformations tab with the origin selected as the refference point then specifying grid easting and northing in the point lable. (see attached)
The solution suggested above using the label styles is the other option for single point comparision.
It is possible to automate this through use of the survey functionality and defining linework codes;
Give one point (say the design drawing) the code B to indicate begining and the surveyed point the code E to indicate end.
Unfortunately you'd have to use excel or similar to define point numbers or place new points below old in the import process (as done attached)
This will give you the required line automatically and you can lable using the above or create a new lable for survey object.