Both are sound trait models and they overlap heavily; the choice is about one factor. HEXACO adds honesty-humility, which the Big Five folds into agreeableness, and it moves some anger and sentimentality between its agreeableness and emotionality factors. If you want to measure sincerity, fairness and modesty as a trait of its own, HEXACO does that; if you want the model with the largest norm samples, the longest research record and the most free instruments, the Big Five does.
Side by side
| Big Five | HEXACO | |
|---|---|---|
| Factors | Openness, conscientiousness, extraversion, agreeableness, neuroticism | Honesty-humility, emotionality, extraversion, agreeableness, conscientiousness, openness |
| Where they differ | Honesty and modesty are facets of agreeableness; anger is a facet of neuroticism | Honesty-humility is its own factor; anger moves to low agreeableness; emotionality is neuroticism without the anger and with sentimentality |
| Evidence base | Decades of research, replicated across languages (Goldberg, 1992, for the markers) | Derived from lexical studies in several languages; Ashton and Lee (2007) make the case that six factors fit them better than five |
| Free instruments | The IPIP-NEO-120, the 50-item markers, the TIPI, and many facet scales | The IPIP-HEXACO and the Mini-IPIP6, both public domain |
| Norms | Large public datasets, used on this site | Fewer and smaller public datasets |
| Where it is weak | Honesty and humility are buried inside agreeableness, so a charming manipulator and a sincere pushover can score alike | Less research, fewer norms, and the sixth factor adds most for questions about ethics and exploitation |
What honesty-humility adds
Ashton and Lee’s argument is that lexical studies in languages other than English keep producing a sixth factor made of sincerity, fairness, greed avoidance and modesty, and that this factor predicts things the Big Five predicts poorly: exploitation of others, workplace delinquency, materialism. If your question is about those, the sixth factor is worth having. For most other questions the two models give the same picture under different labels.
Which to take for which purpose
For comparing yourself with a large published sample, with facets and percentiles: the Big Five, which is what this site measures today. For a measure of honesty-humility as a trait of its own: a HEXACO instrument, which the IPIP publishes free; the owner has held it back from this site’s first release, and the licences page records that. Taking both is reasonable, since each describes the same person from a slightly different angle.