E-6 was a really remarkable breakthrough in image stability. Kodachrome is still better for dark storage, but Ektachrome is quite good. My older E-6 Ektachromes, which have not been stored particularly well, still look about as they did 30 years ago. I understand the stability of Ektachrome has improved considerably since then, which bodes well for the future. I also have some slides made from color negatives that have faded terribly in just 20 years, so color print film (but not necessarily color negative camera film) does not fare so well.
The real basis for choice between Kodachrome and Ektachrome now seems to be on things other than stability and longevity, except perhaps for some special archival situations. Convenience is certainly a factor. But the most important thing is the look of the slides. Kodachrome seems to have a much cleaner and truer look to me than the E-6 films. Of course, some people prefer the garishness of Velvia.