The 1939 Beau Geste was almost completely faithful to the early 20th century romantic novel with much more skillful, nuanced acting and plot development. This version transforms the three Geste brothers into Americans and substitutes a very vague, underdeveloped story line regarding their presence in the Foreign Legion.
However, this is a much better action movie. Telly Savalas is superb as the sadistic sergeant, and the almost thirty year time span between films allowed for a more explicit depiction of the sexual aspect of his twisted behavior. The battle scenes are brutally realistic and the uniforms, equipment, and methods of fighting are much more accurately portrayed here.
The most serious problem with the 1966 version is an absolutely horrid soundtrack. One of the worst ever. The traditional Legion march "Le Boudin" is converted into Lawrence Welk style dentist office Muzak, even though the original, at 171 years old, has long been in the public domain and is featured in most Foreign Legion movies. Actually, "boudin" was a sausage ration issued in the old Legion. The original lyrics are pretty silly (more recent stanzas not so), but, in it's original form, the march is most stirring.
Both films are quite entertaining. Those who want a more coherent story line, more intricate acting, and stronger characters, will no doubt prefer the 1939 version. But for action and realism, this one definitely gets the nod.