Firstly, densitometers do NOT measure dots! Rather, they measure the amount of light reflected from a screened (halftone) area and compare that reflection to two other known values;  paper... by DEFINITION an area whose dot value is ZERO, and  a solid... by DEFINITION an area whose dot value is 100%. Using either the Murray/Davies equations or those developed by Yule and Neilson, the densitometer then calculates and presents a number.
What is not generally understood by new users is the fact that ink is absorbed into the paper. It does not simply lay on the top surface but is spread beneath. It is moved into the fiber of the paper and in effect creates a shadow beneath the surface. This shadow is not seen by a pressman when he uses his glass to look at dot structure. It is, however, seen by the densitometer. It is this subsurface absorption that is responsible for a large amount of the computed (apparent) dot gain.
The Yule/Neilson equation adds an "N" factor to the original Murray/Davies formula. By varying the size of the "N" factor, a user may force the computed dot value to be either larger or smaller. To increase the computed dot value, LOWER the "N" factor. To reduce the computed dot value, RAISE the "N" factor. Typically a "N" of about 1.60.. 1.80 will "correct" for coated stocks.
Generally speaking the "uncorrected", Murray/Davies equation is preferred . Since it allows NO user manipulation, it provides unbiased conversation between manufacturers and users of various inks and papers and keeps the discussion simple. Yes, the apparent dot gain is always considerable. If ink set 'a' exhibits 5% more midtone gain than ink set 'b' then either call and yell at the ink maker, change papers, or adjust the color separations to compensate. Keep in mind that gain isn't bad! Predictable and reproducible gain is a wonderful thing! So long as the process can be expected to behave in a consistent manner -- it is an easy step to adjust the front end. It is unpredictable and varying gain that is a printer's challenge. If the press is not predictable, the pre-press department can never truly tailor their materials. To this end, Murray/Davies equations are generally the best approach where process management and control are the desired results.
Sometimes however there is a need to know how big the dots are 'really'. This is becoming more and more true as assorted digital pre-press systems come on line. Where this is true the Yule/Neilson formula comes to the rescue. Keep this in mind however, where the Yule/Neilson equation is used, each paper/ink combination must be tested and a new correction factor applied.
For most customers, X-Rite informally recommends Murray/Davies.