My, and most photographers I knew, reason for choosing Velvia was that you could develop it yourself. Kodachrome could only be developed by Kodak, but from what I've read about it, it was far superior in every other technical aspect. But not being able to control the push/pull of the development process really limited creative control over the whole process and was a more severe limitation than the higher resolution and color depth that Kodachrome provided.
The way I saw it, Kodachrome was more for consumers who just wanted to press a button and have it done. And Fujichrome was for people who took the process much more serious. Because they could do more with the "inferior" product than relying on the one-size-fits-all commercial process.