TL;DR - These schools have names that refer to different concepts.
From what I could gather, Muay Boran seems to refer to "Thai martial arts" in a broader sense, while Muay Thai refers to a specific art. This is much like you finding a "Karate" dojo and wondering if this "Karate" is better or more interesting than the rival "Shotokan" or "Kyokushin" dojo.
Etymologically speaking, "Muay" refers to boxing and "Boran" refers to something old, ancient. "Muay Boran" thus refers to traditional, or old-style, boxing. In older times, Thai martial arts were localized and often bore the name of the city or region where it was most known. One such example is Muay Chaiya, originating in the city of Chaiya. The name basically meant Chaiya-style Boxing, not unlike the names of the Okinawan arts that eventually became known as Karate (Shuri-te - fist of Shuri; Naha-te - fist of Naha; Tomari-te - fist of Tomari). All of these styles were eventually grouped under the Muay Boran umbrella, including Muay Thai, which is probably the most commonly known of these arts.
That being said, it certainly doesn't mean that the Muay Boran school teaches less effective techniques. Perhaps the instructor there practices a much lesser known style, and referring to it as "Muay Boran" instead of something no one's ever heard of might be more attractive to people that have at least heard the name "Muay Thai". Perhaps this school teaches a more modern, composite style, such as Lerdrit, the martial arts of the Royal Thai Army, or some Thai version of Mixed Martial Arts, incorporating many techniques from different styles to form a complete art. The only way to know is to go there and ask! Who knows, maybe this Muay Boran school actually teaches Muay Thai but chose to use another name for various reasons...
