Like most things in a relativistic universe: it all depends. One man’s Medium is another man’s Book, and one or the other might be more suitable depending on the size used on the webpage. However, because of all the variables involved, I doubt that you can come up with a hard, fast rule that says “Always used Regular for sizes 14px and below, and always used Book for sizes 15px and above.”

Unfortunately, one size does not fit all, nor is your calling plan really unlimited. Welcome to Twenty-first Century America.

A Book in a publication that’s is printed on bad stock by an indifferent printer may turn out looking like a Regular. A Regular printed on expensive glossy paper by a printer who does not know his job may look like a Book.

It depends, in other words, on circumstances. Study those, or work with printers who are knowledgable…

Drat! I've always considered myself a "Book" man, but now, I'm not sure sure. I will lay blame on the Copenhagen Interpretation of Quantum Physics.

On average…

I seem to recall a similar discussion here, in which it transpired that in some faces Book was heavier than Regular, and in others vice versa—which would tend to undermine the principle that an average is meaningful.

Try it with different fonts with both Book and Regular weights and see what you think.

The OP should refine their question a bit. Are they talking about body text, headlines, sub-headers?

sorry, body text. Though at this point I'm not sure it's worth pursuing, given the variability between typefaces?

Well, "regular" can change from face to face, but "book" is always designed to be used in body text.

Digitally, what has both Book and Regular as weights?

Avenir has Book and Roman (Book is 45, which is labelled Light in Univers; both call 55 Roman though.)

Digitally, what has both Book and Regular as weights?

Quite a few FontFonts have both:

https://www.fontfont.com/fonts/celeste
https://www.fontfont.com/fonts/info-text
https://www.fontfont.com/fonts/kievit
https://www.fontfont.com/fonts/max
https://www.fontfont.com/fonts/meta (Normal & Book)
https://www.fontfont.com/fonts/milo (Regular & Text)
https://www.fontfont.com/fonts/milo-serif

The FontFont ones seem slightly thicker than the Regulars, unlike the Avenir one, which is the other way around.

So is the Book weight for printing at smaller sizes (like a multiple masters) over the regular?