ExifTool command (Windows 10) to move files to a separate directory if the modified-date is later than the date-taken

Try this command:
exiftool -d "%Y:%m:%d %H:%M:%S" -r -if "$FileModifyDate gt $DateTimeOriginal" -directory=/path/to/modified/ /path/to/source

This checks the FileModifyDate to see if it is greater than (string comparison) the DateTimeOriginal. If so, it will move it to /path/to/modified/

The -d (-dateFormat) option is needed because the FileModifyDate will always include the time zone of the computer, e.g. 2021:03:26 12:00:00-07:00, while DateTimeOriginal does not include a time zone, e.g. 2021:03:26 12:00:00, and that would cause FileModifyDate to be greater than DateTimeOriginal if the time stamps were otherwise identical.

If you need to deal with filename collisions, you can add a copy number to any additional files by switching from -Directory to -Filename and adding some percent tokens which are detailed in the -w (-TextOut) option. In this case, any additional copies will have an UnderscoreNumber added to the filename.
exiftool -d "%Y:%m:%d %H:%M:%S" -r -if "$FileModifyDate gt $DateTimeOriginal" -Filename=/path/to/modified/%f%+c.%e /path/to/source

The quoting for this command assumes you're using CMD. If you're using PowerShell, I believe you need to swap the double quotes for single quotes to prevent PS from assuming the dollar sign is the start of a variable.