It's a difference in the way winamp and fmod play the song Spitfire, these old trackers all have thier differences and different sound effects used, especially in chip songs where they are more noticeable sound different in different trackers.
Luckily it is easy to fix.
You could try the resources page;
http://www.dbfinteractive.com/downloadmenu.phpLook for utilities for a file called mod 2 xm
This is what I have done to the song for you, I attached it to this post, I converted it to XM and then changed the file back to .mod so it still works with your program.
Cool too that you are making a remake

It will need to be one single file btw.
Anyway, hope that helps.