HOD Bill,
Don't worry about such things as "authenticity", because both lines are nothing if not authentic.
The D&S operates the Silverton Train, which has been providing uninterrupted seasonal service to Silverton since 1882. Can't get more authentic than that, because the line hasn't ever been down by abandonment. You have to accept @#$%&, and tourists today in place of other golddiggers and rubes of times gone by.
The C&TS is absolutely authentic too, but in a way that is more time dated. Everyone else has already talked about that.
The answer you are looking for, however, is that the Silverton Branch follows the Animas River all the up to Silverton, through some really beautiful scenery that can only be seen by train. Pictures and video smply can't do it justice. The C&TS is completely different, as has been touched on by a couple of others, but mostly because of the diverse scenery. The C&TS traverses across different watersheds, and the terrain ranges from high mountain meadows and Toltec Gorge to high desert and badlands.
Both are absolutely required, and 100% "authentic". Ride for the trains and their historical significance and importance. They were the same railroad, and what you see today is simply an extension, a version, if you will, of what you would have seen 50 or 75 or 100 years ago.
And don't forget to squeeze in the LaVeta line if you have time, for exactly the same reasons!
Enjoy yourselves.
Mike