Is there a tool that can take two folders of images files and give comparison (duplicates info) based on images' EXIF data, instead of comparing file size or file dates (which tend to be unreliable since they can relatively easily change with file operations, while the actual images do not)?
Yes, there is, but you will need to be comfortable with the command line to do it. It will work best if you are in a unix/posix environment. This is available for Windows as an add-on using cygwin.
The program is exif tool Instructions for getting and installing.
You will want something like
exiftool -CreateDate /path/to/folder/*.jpg
It will spew the filename and the create date of each.
Do this for each folder. Sort the two lists together. Now look at the corresponding files that have the same date.
*** Method 2.
Create a temp directory
Copy the content of both folders into it.
Use a program that reads the creation date out of the file. (Aperture does this)
Files with the same date will show up next to each other.
Note: Different programs that edit images do not respect all metadata. You have to do substantial sanity checking on this sort of project.
Note: If you start with a raw format, process it into a JPEG, then the createfile time stamp of the JPEG may be the same as that of the raw file, or that of the time it was created. (Software should only change the Modify tag)
Note: If you are mixing up files, you want to be able to get back to where you were. Lot to be said for giving each file a keyword as to it's source: E.g. keyword folder:/path/to/folder1 for the ones that were originally in folder 1.
Note: exiftool allows you to rename files. You can rename files as date-stamp-original filename. This would make the files sort alphabetically in the order they were created.
It's really easy to shoot yourself in the foot. E.g. if you rename files to the date stamp, then if you have 2 shots with the same time stamp, one is overwritten. Exiftool can protect you from this with an incremental counter.
On macOS and Linux you can use the command line tool
which is excellent