🚀 go-pugleaf

I use both a lot, but there is little overlap between what the two do. 

FM>ID: equation editor, table styles, conditional text, footnotes, simple and complex and independent numbering systems (outlines, separate numbering for figures and outline, etc.), headers and footers, sideheadings, variables, run-in heads, crossrefs, and multiple placement options for inline graphics. 

ID>FM: better colour mgt, exact placement of images and image crossing pages (can be done only awkwardly in FM), much better typography, use of extended characters for OTF's, native psd and ai file placement, transparency, much better clipping options for graphics, text on a path, drop shadows, options for detail of viewing of placed images, better scripting language, and gradients. 

I'm sure there are more differences, but if you are creating a book, especially one with numbering options, use FM. For a magazine, handout, etc., use ID.