When I was working a little on the lower levels a few weeks ago, I found that
234 in the enneagram correspond to what Freud refers to as the superego, and what cognitive theory talks about as Te and Fe. It primarily discusses who we are around others, feelings such as caring and shame, and how others see us, but it also talks about personality and identity expressions. 2 would be a typhical negotiator response, 3 would be a typhical director or explorer response, 4 would be a typhical builder response.
567 in the enneagram correspond to the world, and how the world moves us and what emotions it triggers in us (Ne and Se) It primarily discusses emotions such as anxiety and joy/enthusiasm. 5 would be a typhical negotiator response, 6 would be a typhical builder response, and 7 would be a typhical explorer or director response.
891 in the enneagram correspond to the ego. (Ni and Si) and emotions such as dissatisfaction/satisfaction. How we see the world and how we want the world to look. 8 would be a typhical director response to the ego, 9 a typhical builder response, and 1 a typhical negotiator response.
The Sx, Sp, and So correspond to our Id. (Fi and Ti) Our self protective mechanisms, our sexual desires, self-control, the ability to analyze and study our emotions, and responding "appropriately" to our needs. Sx would be a typhical explorer or director response, the sp a typhical builder response, and so a typhical negotiator response.
Which would mean that Freud, Isabella Briggs/Beebe and Enneatheory are talking about similar levels.
There's three hidden types in the ennea-system, the instinctual types (sx, so, sp) and currently I'm working on building them in and expanding the enneagram from the nine classic, to the twelve types. The biggest reason I'm doing this is because they correlate to what I call ideologies in ripple studies, and I want to combine/merge the two. The enneagrams biggest strength is that it's much more social. It's best described as our ingrained thought/emotional patterns.