When it comes to restaurants, beverages and appetizers are the first things ordered so it's important that those are easily found. When it comes to hierarchy and first impressions of a menu, it doesn't seem that they take priority in hierarchy
The vintage look of this menu combined with the photographic elements really gives the feeling of a smokehouse BBQ. I also like how one page of the menu is a different color, it really grabs your attention.
A very artsy and strong design perhaps could use some color but is overall very strong. Important areas are highlighted or are bolder while various typefaces add flare and variety. The overall layout is thought out and well organized.