For what it's worth, the 5963 has a higher-purity cathode, making it suitable for computer operations where the tube may be cut off for extended periods. Often in audio, these oddball requirements make a tube that sounds better; this is one of those times.
And yes, I did learn to program an IBM 709 computer which was tube-based - the 7094 was the transistorized version. This would have been the early sixties, when I was in high school. The computer occupied the basement of the Mechanical Engineering building at the University of Washington. Legend had it that there was one person whose full-time job was to go up and down the aisles with a shopping cart of spares, replacing tubes before they wore out. I never met the person, so I can't confirm the story, but I still tell it anyhow. :^)