Based on n = 290, I found this correlation matrix in Gaughan et al (2012) (I think the adjusted R-squareds are for regression models predicting domain scores from the domains of the other measure; e.g., 50% of variance in honesty-humility was predicted by the five NEO domain scores).
Summarising these correlations, focusing on the HEXACO:
- Honesty-humility is most closely related to agreeableness but is not the same
- Emotionality is related to neuroticism, but also quite distinct the correlation is much weaker than would be required to argue it is a similar construct.
- Extraversion is mostly the same in both models, but hexaco extraversion seems to be more related to neuroticism (-) than NEO neuroticism.
- Agreeableness (HEXACO) is moderately related to NEO agreeableness, but there are clearly differences. HEXACO agreeableness also has a notable correlation with neuroticism (-).
- Conscientiousness is mostly the same in both models.
- Openness is similar in both models, but not massive.
Focusing on the NEO
- Neuroticism is distributed across hexaco emotioanlity, extraversion, and agreeableness
So in summary
- HEXACO Extraversion, conscientiousness, and openness can probably be related to a similar interpretative framework as the NEO/Big 5 literature.
- Relating HEXACO to NEO agreeableness and neuroticism is difficult. Using emotionality as a proxy for neuroticism is definitely problematic.
Another empirical study
Here was another study I found in Ashton et al (2014) using Big 5 markers.
Correlations between honesty-humility and agreeableness were not as strong as above. Also, the negative correlation between neuroticism and extraversion was much smaller.
How it is discussed in a paper
I found this paragraph from Dunlop et al (2016) to be a good quick summary of the differences:
Within the HEXACO model, the Openness, Extraversion, and
Conscientiousness factors generally correspond to their Big Five
counterparts. The Emotionality and Agreeableness factors of the HEXACO
represent rotational variants of Neuroticism and Agreeableness in the
Big Five. However, the most prominent difference between the HEXACO
and Five Factor model is the addition of the HEXACO Honesty-Humility
factor ... (Ashton & Lee, 2007; Ashton, Lee, & de Vries, 2014).
- Gaughan, E. T., Miller, J. D., & Lynam, D. R. (2012). Examining the utility of general models of personality in the study of psychopathy: A comparison of the HEXACO-PI-R and NEO PI-R. Journal of personality disorders, 26(4), 513.
- Dunlop, P. D., Bourdage, J. S., de Vries, R. E., Hilbig, B. E., Zettler, I., & Ludeke, S. G. (2016). Openness to (reporting) experiences that we never had: Overclaiming as an outcome of the knowledge accumulated through a proclivity for cognitive and aesthetic exploration. Journal of Personality and Social Psychology.
- Ashton, M. C., Lee, K., & de Vries, R. E. (2014). The HEXACO honesty-humility, agreeableness, and emotionality factors a review of research and theory. Personality and Social Psychology Review, 18(2), 139-152.