Hi, I am doing the same thing when I clean up my game collections so for DELETING the following steps work. See this:
#1 File Names are identical but extensions are different (x.zip and x.jpg). You have cleaned up all the ZIPs in source, but now want to delete the JPGs in destination. Use "Edit - Select Other - Select Source All to Destination (Ignore Extension)". This will select all the JPGs you need. You can then either copy these whereever you want them OR do "Edit - Invert Selection" and then delete the JPGs you do not need anymore.
#2 I had the special case where I had "x.zip" and then "x-thumb.jpg". For this the friendly folks here wrote a script that would select exactly all files that are not represented as a "stem" in the other, The final script that works fantastically is here: Select files in Destination that START with the filenames in Source - #10 by lxp Scroll up there to see my request and how it works. Thanks again, @lxp