The difference comes in when you use the same image multiple times on the same or different pages.
Let’s say you use an image on all of your pages, a logo perhaps. If you use a regular image stack, then a visitor’s browser will download that image from the server each time you load a new page. It’s a unique image (filename & path) A regular image stack creates a new image file for each instance of an image, even if it’s loaded with the same source image.
If you use a site image, then the image will be loaded only once. The visitor’s web browser will see it as the same image and just load it from the browser’s cache.
Unless you need editing, I would use the new, default, site image.
I’d use the new default site image unless you need some of the resizing features of the old style image. It’s just plain faster and stores all images in the single resource directory.