It is glacially slow. It takes a few hours to parse 10k+ files.

There is nothing in your description of your algorithm which suggests it should take anything more than a few minutes at the most to run and move 10k files, unless where you are moving them to is on a different filesystem or there's some other important detail which has been omitted. Did you profile your script to find where the bottleneck is?

if ($a eq $b) - works, as expected. But (if $a =~ /$b/ ) does not.

Define "does not". One is a string equality while the other is a regular expression match. They are designed to perform different tasks. Have a read through How to ask better questions using Test::More and sample data which might help us to help you. Clearly here the way you have written them the second expression has dodgy parenthetical syntax but that's probably just a typo in your post.