For you to be the most helpful in this investigation, the rest of us need to know how your BC was produced. To my eyes the Obama BC was produced electronically, not by printing letters on top of a "blank". The difference is critical, many places use a blank from a printer with the background, put it in the printer and print the text on top. The Obama BC was produced electronically (not photoshop) by writing the letters onto an electronic blank. If that's what yours looks like, it would clear up the origin of his.
The difference between the two should be very clear with a magnifying glass.
It contains a link to a website that translates official documents from one language to another. It contains a link to a Hawaii marriage certificate that looks like it's printed on the same paper stock as the COLB, but with a different top banner heading. The computer fills in the form labels and data. Note also the top space is used for form information, so the location of folds makes sense. Also, the site has a slightly larger image on it -- just replace the word small with big in the filename.
-PJ