Do old patients like those old doctors more who talks to them more, when they get a feeling that he is respecting their age, any psychology behind this ?

See below: Speaking from my experience: i work primarily with geriatric clientele and i'm much younger than my average client. It's not about the age, it's about ability to relate, empathize, respect, and being able to help on the person's level. While having similarities definitely helps with establishing rapport, ultimately it's my ability to relate, empathize, and be a clinician a that helps the client.

Depends: People are all different. The relationship between patient and doctor depends on many factors. Each person wants something to match their own needs.

Cohort effect : It sounds like what you are talking about is what is known as cohort effects. Cohort effect occurs when people feel comfortable relating to other people of similar age or growing up in a similar era or environment. They feel a sense of commonality because of the similarity between themselves and the other person.