The two main 19th century styles of text face, Modern and Old Style (which ironically came later) are pretty generic.
So Century OId Style is what one would expect a modern face, Century, to look like, given an old-style treatment.

Most interestingly, it creates a huge scale of page.
Check out the large size in the 1925 Linotype Manual to appreciate how tight it sets, both in horizontal fit and vertically (as you note), it blows avery other face in the manual out of the water.

It was well used for these qualities in the 1960s, 70s and 80s in advertising and brochures—making it far more popular, in my experience, than Bookman.

I used Century Old Style quite a bit in the early 1990s as both a text and display face, but Bookman in its various manifestations always struck me as being too crudely fitted for nice typography. But perhaps people today are more appreciative, given the present interest in slab serif styles.

Phemister’s Old Style for Miller & Richard became one of those iconic faces of its period as to be practically generic, and it spawned a number of imitations/inspired-bys. Century Oldstyle and Bookman Oldstyle are but two, evolving in slightly different directions.

According to Mac McGrew’s ’American Metal Type Faces of the 20th Century’ Bookman Oldstyle is a result of thickening the strokes of the original Miller & Richard design. The contrast, in particular, is much reduced. The ATF version shown from 1906 looks pretty much like itself, including the popular swashes. The low contrast allows for those meaty swashes, which are the blessing or curse of many shop signs.

The descenders in the ATF version are even more squashed than later versions.

I do see now that I made one important mistake: I failed to realize that Old Style and Old Style Antique were two different faces, and the latter one does resemble Bookman.