You might consider using a clone detector such as our CloneDR. This tool parses large sets of computer program (HTML is special case) files, builds abstract syntax trees representing the essential structure of each files, and compares programs for similarity.
Because it is comparing essential program structure, it ignores inessential differences such as comments and whitespace, and deterimines that two code segments are either identical or one can be obtained from the other by substituting other blocks of code. The latter allows the recognition of code that has been modified in various ways. You can see samples of clone detection runs on a variety of computer languages at the web site.
In your case, what you would be looking for are files in system A which are essentially clones (exact or near misses) of files in system B. As a general rule, if a file a is a variant of file b (e.g., with a few changes) the CloneDr will report it as a clone and show the exact differences.
At the scale of 20,000 files, I can see why you want a tool, and I can see why you want near-miss matches rather than exact matches.
Doesn't run under Linux, but I assume your problem is hard to enough to solve so that isn't what you are optimizing.