"Rio Bravo" is a great western. "Fistful of Dollars" is a great western. "True Grit" is a great western. Hang em High. High Plains Drifter. All great westerns. The westerns that high falutin types think are great are usually just dramas in cowboy boots. A real western is what it is.
I disagree. All films are (or should be) judged on the same criteria. The genre is (or should be) immaterial to the process. A truly great film transcends its genre. All the films that you mentioned are great westerns, but great westerns only appeal to people who really appreciate westerns. A truly great film that happened to be a western would appeal to people who didn’t particularly like westerns! In the same way, I’m not a great fan of musical fantasies, but I think “Wizard of Oz” is a great film. To use your analogy, its not a question of whether you prefer a good hamburger or a good steak, its whether you prefer good cooking :)
Now of course this doesn’t happen in reality, because there is a lot of snobbery in film (and in the arts generally, in fact). As an example, check through the list of Oscar winners - very few westerns win awards (out of favor). Very few children’s films win top awards (if a film is for children, people think it must therefore be childish, which is nonsense). Comedies are seriously underrepresented too (people think a serious award should go to serious films - also nonsense).