For my work I often need to copy files between 2 directories or compare the content of 2 folders to see what the differences are (files, size, creation date, etc..).

This currently requires opening nautilus twice and scaling the windows so that each takes one half of the screen.

My suggestion is to have an option to split the file listing in 2.  A button/setting toggles this dual list on and off.  Support for DragNDrop between the 2 listings and each being able to navigate to a different directory.  Other than that the normal file list capabilities can be retained.  Perhaps as a minimum support vertical split and optionally horizontal split view.