Hi,
Normally, I would recommend that if the two layers are overlaying reasonably well, to ignore the difference coordinate systems. If you want to update the coordinate system of one layer, use the Define Projection tool, or add both to ArcMap, set the data frame to the coordinate system you want and right click the other layer in the table of contents and select data, export data (pick the use-the-data-frame option).
However, the differences between NAD 1983 and CORS96 should be relatively small--about a meter at most. How much of a difference are you seeing? If it's more than that, something else like an incorrect coordinate system definition may be happening.
Melita