@Avelino Automatic insert only works when the image is attached to the post. You can tell if the image is attached to the post by looking at the media library. There is a column that lists which post an image is attached to.
Duotone actually displays some EXIF information as well, but it also only gets the EXIF if the image is attached to the post. You can see in this screenshot duotone exif is on the left and Exifography is on the right.
The only other way to display EXIF without having the image attached to the post is to use the shortcode with the image ID in it.