It's true, Kodachrome is undisputably the most archival film in dark storage, but its light-fading characteristics leave something to be desired. In his authoritative book on the subject, "The Permanence and Care of Color Photographs," (Preservation Publishing Co., 1993, ISBN 0-911515-00-3) Henry Wilhelm states that Kodachrome slides projected for very short periods of time may be projected many times without showing noticeable fading; however, Kodachromes that are projected for several minutes at a time may fade noticeably after as little as 45 cumulative minutes of projection. Incidentally, Kodachrome's cyan and yellow dyes are quite stable -- it is the magenta dye that is problematic. Wilhelm notes that if Kodak were to develop a new magenta dye, Kodachrome could easily have both the best dark stability and the best projector-fading stability of any transparency films. Of course, that was in 1993, and we all know Kodak is not going to put any effort into improving Kodachrome now. I will quote an excerpt from the book's recommendations for color transparency films:
For the photographer who prefers Process E-6 films, Fujichrome films are clearly the best choice. Fujichrome's resistance to fading during projection is the best of all slide films -- for a given amount of fading, Fujichrome slides can be projected twice as long as Ektachrome slides. However, when [the] yellowish stain that occurs over time in storage is considered, Fujichrome's stability in dark storage is roughly equal to that of Ektachrome films. ... Kodachrome has the best dark storage dye stability of any color film, and Kodachrome, as a result of its unique, external-coupler processing method, is the only color transparency film that remains completely free from yellowish stain formation during prolonged storage in the dark. Unfortunately, however, Kodachrome has the worst projector-fading stability of any color slide film on the market.
The "yellowish stain" he mentions is a result of the chromogenic development process of E-6 films; undeveloped dye couplers that remain in the emulsion after development may over time discolor and stain the emulsion. Keep in mind the book was written in 1993; since then, this problem has allegedly been reduced. It's also questionable whether this was ever a great problem. Personally, I have several hundred Ektachrome and Fujichrome slides from the '70s and '80s in my collection and I don't believe any of them exhibit this staining.
It should also be noted that in the past 10 years both Kodak and Fuji have worked to greatly increase the stability of E-6 films. It may no longer be fair to say Fujichrome is "clearly the best choice." Rather, I think both films are at the point now where either one would be an excellent choice and would certainly outlast the photographer. If you don't do much projection, don't mind the expense and difficulty of obtaining processing, and find its color rendition attractive, Kodachrome may be a better choice. These days, one other factor that should be considered is the convenience of digital scanning. Fujichrome films are usually reported to scan better than Ektachromes, and all E-6 films are easier to scan than Kodachrome.
Whatever you choose, just don't buy it at Wal-Mart.