In order to compare two fields in two different files, you need to be able to join the tables together on a common key (perhaps an ID field or equivalent)
Add a field to the destination table to put the comparison results.
Once joined, then you can perform an equality check using the field calculator
You indicate that you need to do this with an arcpy solution. The best way to do that is to examine the code snippets for the basic tools (ie Add Join, Calculate Field etc). If you have made progress on that front, you might want to include it in your post.