Many endeavors have disputes over who are the greats in the field. Baseball aficionados have argued for decades over the greatest players and teams. Complex statistical analyses have been devised that can be used to compare players from different generations to each other. Others statistics rate the comparative values to their teams of pitchers versus position players. Avid readers rate famous authors based not just on how much the reader likes the writing but on the writer's impact on literature. And similar evaluations exist in the field of arts criticism and music.

Perhaps because philately is a discipline without an academic footing, little attempt has ever been made to compare the great collectors in the history of our hobby to determine the ones who have been the most important and why. The issue is best looked at in two parts. Until the death of Alfred Caspary in 1955, the criteria for whether a collection was great or not was how comprehensive in scope and how complete the collection was. Besides Caspary, the other two collections in the pre-1955 time frame that compete for the crown of "Best" were the Tapling collection, now in the British Museum, and the Ferrary collection that was sold after WWI to pay German war reparations after the French government confiscated the collection from the Ferrary estate.
Since 1955 and the death of Caspary, there have been no attempts to collect world rarities complete. Even the wealthiest and most avid collectors today restrict themselves in some degree by area and era. The reason is probably that even by Alfred Caspary's time what he was trying to do was all but impossible. Tapling, who died in 1891, and Ferrary, who died before the end of WWI, put their collections together in a period when stamp collecting was much less popular than it was later (and than it is now). It is no longer money that prevents anyone from having a complete collection of the world's philatelic rarities. Even if you had $500 million to spend (and some do), the diffusion of philatelic rarities throughout the stamp world, many in hands of people who will not sell in their lifetime, has made the creation of such a complete collection impossible.