You might want to be more specific on which version of the book, my 22'nd edition ARRL Antenna Book, Chapter 3 page 12 finishes up a section called "Real Wire Radial Systems" and starts a section called "Optimizing Radial Lengths". I did read through the entire chapter, and while there are sections on both vertical and horizontal antennas, the two were not directly compared or were their plots shown directly against each other. Apparently we have two different versions of the book.
It does explain how the effects of ground affect both types of antennas in different sections of the chapter, and there are some definite differences, but that is as close to a direct comparison as it gets. It does not directly compare one polarization to the other, and doesn't have the two polarizations in the same figure.
I would also point out that it assumes ground mounted vertical antennas in most of its discussions, which will have some distinct differences from an elevated vertical ground plane antenna.
Returning to the discussion at hand, when looking at height, typically it is easier for someone to get a vertical antenna mounted higher then a horizontal antenna, in some cases significantly. This would only help the vertical antenna.
There is also the fact that you are effectively comparing apples and oranges. Horizontal and vertical antennas have different properties, and if you have two antennas will complement each other very well. But because of the different properties presented directly comparing the antennas becomes very difficult when comparing for DX purposes. Other variables will have more of an effect, and these variables can make the antenna with more gain (whichever one it may be) near useless while the antenna with less gain has no problems at all.
In any case, either should work, but if the op can have both a vertical and horizontal, and easily switch between the two antennas, that will work even better.
The DB