It depends on the type of analysis. For mats, combined footings and grade beams, we often give vertical subgrade reaction in units of F/L^3 an it is just one fixed value. This is based on Hetenyi's book. Also for mats there are detailed equations if the soils are cohesive & for various footing shapes (Ref. 3).
For laterally loaded pile with single shear load & for embedded retaining structures like sheetpiles and soldier beams, we give a horizontal subgrade reaction per each soil layer. In general, lateral subgrade reaction is 1.5 to 2 times the vertical subgrade reaction. To obtain lateral subgrade modulus, multiply the lateral subgrade reaction with pile or pier diameter or width.
One detail to keep in mind is to follow one researcher's method. For example, I use Blum's method for cantilevered and tiedback soldeir beams. It is also possible to analyze cantilevered pole type structures using other methods like Teng, IBC, Czerniak, Broms and others. Just be careful on mixing analysis of two different methods under one calculation module.
There is no comparison between lateral subgrade modulus, LSG, and passive resistance, PR to my awareness. If you use LSG, then you need to check for maximum lateral deflection at the ground surface. If you use PR, you need to check that the induced soil pressure from the lateral load does not exceed the soils allowable passive resistance.
The following texts cover your topic:
1- "Single Piles and Pile Groups Under Lateral Loading", Reese & Van Impe, 2011
2- "Foundation Analysis & Design", J.E. Bowles, 1995
3- "SP-152: Design and Performance of Mat Foundations", ACI, 1995
4- "Foundation Analysis" R.F. Scott, 1981
5- "Analytical and Computer Methods in Foundation Engineering", J.E. Bowles, 1974
I also understand Budhu and Poulos have their own methods.