Yes, if I want the original Kodachrome it's not because it's a better film by accurate reproduction standards. It's because I just like the look of it.
Kodachrome II, 64, etc. are better films and processes in that they more accurately represent what our eyes actually see.
Compare, for instance, the following WWII era original Kodachrome photo:
With the following modern Kodachrome shot (one of the last...):
The first has a very soft, pastel look - it almost looks like a Norman Rockwell painting!
The second is a much better reproduction of actual colors - lean in close and you can't tell it from real life. So it's a better film by that standard, but it doesn't have the unique charm of the original.
Here's another question: I've seen a lot of Kodacolor prints from the same era as original Kodachrome that have the same vibrant, pastel look. What's up with that? Kodacolor II stuff from the 60's and 70's usually looks pretty bland in comparison.
But of course this is all moot, as Kodak is 5000% less likely to resurrect the original Kodachrome than K-14 type.