The first criteria is that our personality matches the characteristics measured by that system. In other words, it fits into a category most neatly. For example, in Buddhist psychology there are 3 types, each of which have a positive and negative (or skillful/unskillful) expression: Hatred/Wisdom, Craving/Compassion, and Delusion/Speculation. I have some pretty definite Hate/Wisdom type characteristics, so I like this system. (I suppose I also like it because I am a Buddhist, and because it is so simple.) People who are more balanced across the various categories, who therefore aren't easily categorized, aren't going to be as interested.
The second reason we like one system over another is when we get put into a category of which we approve. For example, I'm not so into Chinese astrology, probably because I was born in the Year of the Hare. But being "The Performer" in Meyer's-Briggs (Jungian) is just fine. In the Buddhist system, people who are mostly "Delusion/Speculative" types seem not to like the system very much!
Here is where I fit into other systems I know about:
- Enneagram: Enthusiast or Epicure (7)
- Myers-Briggs: "Entertainer" (ESFP)
- Western Astrology: Leo
- Chinese astrology: Hare
- Compass: Northwest
- Buddhist psychology: Hate/Wisdom. There is another, simpler version of this, in which I would be a "Dharma Follower"
There are other reasons we may like or dislike these various systems. Some of us don't want to be pigeonholed, which is fair enough. What does it mean about a person if they like to learn about systems of psychological types, or if they don't?
A little more info about Buddhist psychological types in this 1970 Lecture by Sangharakshita:
The Question of Psychological Types
Here is a funny video about types made by Trey Parker and Matt Stone, with the help of an original recording of Alan Watts.
This is an interesting book that goes into Buddhist as well as Ayurvedic psychology in relation to working with depression, "The Chemistry of Joy" by Henry Emmons M.D.
(Image "Freud" by Andy Warhol.)