I was going to extract each verse into a database (I have access to many-a-sql-server) from the PDF and the website. Normalize the verse - that is take out all of those cross referencing symbols and make sure spaces are the uniform (I'm sure extracting the text from the PDF might cause excessive whitespace). Then using a diff program like Simon suggests, and finally just displaying it all back out in another PDF, formatted with OLD verse and NEW verse side by side. Highlight the changes.
Buuuuttt.. you want to categorize the changes it looks like. That's what it seems like to me... some change types are more interesting to you, I guess?