I can't answer your question as to which of the two barrel lengths is more authentic, but I need to make a suggestion if you're planning on using the rifle for Cowboy Action Shooting. I suspect the 16" barrel won't hold ten rounds in the magazine tube. Make sure that whatever rifle you choose can hold ten rounds in the magazine tube. Most stages call for ten rifle rounds, and if your rifle holds fewer, you will have to reload on the clock. This will put you at a severe disadvantage.
Don't wait. Join a CAS club real soon. It's a hoot!