Modern or older period pieces. Which are more authentic

Westerns are a good example. Take a couple of old westerns like Shane and Searchers which were made during the 50s. Now compare these with 2 from the modern era, like the remakes of True Grit and 3:10 to Yuma made in the 2000's. All these movies take place in the late 1800s. But which feels more authentic to the time period? The modern made ones with the more expensive set, costume and production design with sleeker, crisper cinematography? Or the older ones made in the 50s which are closer to the actual time period of the movie and have the grainy, archaic cinematography with simpler set design due to budget and limitations of technology at the time?

For me I prefer the older Westerns and by extension older made period piece movies. Any film made nowadays thats set in the 1800s or early 1900s doesn't feel visually authentic, even though a lot of effort and money has been spent to recreate the time period its set in with great detail along with state of the art camera tech.