According to the Story Grid by Shawn Coyne, the core value in a westerns concern the following: the individual within and out of society, strong vs. weak, and civilization vs. wilderness. The core piece of a western is the showdown between the hero and the villain. There are a few different kinds of westerns.
The Classic Western- A stranger comes to town that no one quite trusts, but it turns out they’ve got some sort of unique ability or skill set that makes them the perfect person to save the town from a big bad. In the end, the town sees the value in the stranger and welcomes them to stay, but alas, the stranger must move on. Besides all the classic westerns that fall into this genre, this arc pops up as a sub genre all over the place. Vampire Hunter D used it, so did Full Metal Alchemist.
Vengeance- is mine, sayeth the Lord. Sorry, knee-jerk quote finishing. Anyway, this time the stranger isn’t just passing through, s/he is there to right a specific wrong. This is more the overall arc of Firefly.
Transition- The hero starts in a society and ends outside society. You see a lot of echoes of this sub-genre in dystopian fiction.
Professional- This is really more of a cross-genre to the professional sub-genre in crime. The hero isn’t trying to save society, they’re just making their living outside the law.
Westerns have very successfully resurged through genre blending with science fiction. Firefly is possibly the most overt Western-Sci-Fi blend, but if you think about it, pretty much any story set on the outskirts of society in space, exploring and pushing further out of the comfortable bounds and dealing with the clash between the existing society and the encroaching society fits into the western story arcs. Ditto for post-apocolyptic or dystopian stories where the protagonists leave society or attempt to piece together one in a wild, lawless land. It’s really interesting seeing how the elements of what looked like a dead and dying genre came back to life.