If both pictures (15mm and 800mm) were taken from the same distance, and you crop in the 15mm image enough (supposedly having infinite resolution in the image), you would achieve the same image as the one taken with 800mm.
Except maybe for the depth of field, that I still have to think about, I'm still not versed on this topic of depth of field - aperture equivalence between focal lengths. I know what f/XX means, I know what it does on the depth of field, but have still to think about it thoroughly to be sure.
Now on the 'telephoto compression', I always understood it as the capability of a telephoto lens to show foreground, subject and background somehow 'closer' to each other than it is, simply by using a very narrow angular cropping through reality. And a good amount of depth of field if one does want foreground and background in focus, to achieve fully this 'compression' effect. With shallow depth of field, this 'compression' is less visible, and the subject is simply isolated by foreground and background blur.
I do not venture on the topic of 'proper distance to look at a print' and effect it can produce, nor if there are rules to respect there.
Greg