In reply to Fredt:
Most jpegs have some detail about the quality and the encoding process used to create them in the exif data
There's at least 40 lines of info in the exif data on a photo taken by by camera phone, and 177 lines of info on one taken on my Nikon D3100.
Obviously a lot of that is about the camera, focal length, lens, ISO rating etc, but there's some stuff about compression and quality
So, you could extract all the exif data from one of your originals and then from the "same" file that's been converted and see if you can spot the differences there...
Not sure what tool you'd use in your OS, but in linux "exiftool" spits out loads of info on each file.
Also, I think some jpgs include thumbnails. Your conversion program might have stripped those out?