It can make a huge difference.

    `convert from_camera.jpg -resize 200x200 resized.jpg`
    `exiftool -all= resized.jpg -o resized-exif-stripped.jpg`
    
    from_camera - 2.4M
    resized.jpg - 33K
    resized-exif-stripped.jpg - 16K

In this simple example, the EXIF data double the file size of a 200x200px thumbnail.