Good methodology for upgrading a large/complex sites?

I don’t know of a great before and after comparitor that would get you the results you need. In fact I would be worried that any tool like that won’t catch any failures in functionality.

Honestly I would suggest incrementally building up a testing suite that goes through some of your standard processes and verifies the results and then just run those scripts every time you do an update.
Such as:

1. Create new page
   • add text
   • add image
   • add link
   • publish
   • verify text change
   • verify image
   • verify link

Do the same thing for new post, then do all of the above plus verifying that you can edit text and links on previously existing posts and pages.

Selenium is a decent tool. You can also build out the automated tests in Python or whatever language you love best.