Gallery Fake, Bartender Recommendations
The episodic nature of both shows is the biggest similarity. In each show the main character helps a new person each episode. Each episode also teaches something. In Bartender, the viewer gets to learn a lot about the histories of different types of alcohol and different types of cocktails. In Gallery Fake, each episode teaches about an artist or a style of art. Both shows are generally laid back and calming, since each show usually concludes with a problem being solved.
Both are slow-paced, episodic, seinen anime based on manga and both have a similar feel. Protagonists are similar in that they both pay attention to minute details. Bartender is a bit more mature and serious in my opinion.
Both Bartender and Gallery Fake present information about their respective subjects (various drinks and alcohols in Bartender, and various pieces of art in Gallery Fake) while still managing to be greatly entertaining. You learn something every episode, sometimes without even realizing.