diff two directories, but ignore the extensions

I've got two directories with similar file names but different extensions. Here's an example:

DIR1:
 - IN89284.wav
 - OUT9920.wav

DIR2:
 - IN89284.mp3
 - OUT9920.mp3

I want to compare these directories but ignore the file extensions, so in that case they would be the same. How can I do that? I guess that I'd have to loop through the first directory, trim each file name (cut the extension) and then search for it in the second directory. Is there any better way to do that?